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The integrated industrial control systems require a reliable communication among each part of control systems. The limitation of network topology comprises the low latency of data transmission. The network algorithm topologies are sometimes failed to ensure the faulttolerant network design even if they offer it. Therefore, this works investigates a Node Insertion Algorithm (NIA) and Ant Colony Optimization (ACO) in order to solve the Travelling Salesman Problem (TSP) for network topologies in a communication network. The NP Non deterministic (polynomial time)-hardness based of TSP leads to the impossibility of polynomial time algorithm to solve an exponentially increasing amount of communication addresses. TSP itself is a well-known solution method known in the graph theory which is based on approximation algorithm. Therefore, this work also presents a comparison between the NIA and ACO for 200 nodes of network topologies. The results show that NIA is superior than ACO in terms of resulting ring's cost and computation duration. Three topologies are tested and it is observable that NIA requires only 14.88 seconds to finish the computation in which the resulting ring's length reaches 164019 units. Therefore, the achievement of the NIA can be applied for logical and physical nodes for a reliable connection in an industrial topology network. [ABSTRACT FROM AUTHOR]

Raman spectroscopy is an effective method for diagnosing the aging state of transformer oil-paper insulation. Aiming at overcoming the drawback of previous methods that require a large number of training samples, this research proposes a method for aging diagnosis of oil-paper insulation that can be used for few-shot learning. In this study, different Raman spectroscopy samples of aging insulating oil are obtained by accelerated thermal aging experiments. This paper uses identity matrix as node feature, calculates the connection weights between them by Gaussian kernel function, and constructs the graph structure of Raman spectroscopy library. Using graph convolutional neural network (GCN) based on the graph structure, a diagnosis model is established. The diagnostic accuracy rate is as high as 95.5%. This method provides a theoretical basis for establishing a new structured Raman spectroscopy library and assessing the aging state of transformer oil-paper insulation with a small number of training samples. [ABSTRACT FROM AUTHOR]

Signal processing is a very useful field of study in the interpretation of signals in many everyday applications. In the case of applications with time-varying signals, one possibility is to consider them as graphs, so graph theory arises, which extends classical methods to the non-Euclidean domain. In addition, machine learning techniques have been widely used in pattern recognition activities in a wide variety of tasks, including health sciences. The objective of this work is to identify and analyze the papers in the literature that address the use of machine learning applied to graph signal processing in health sciences. A search was performed in four databases (Science Direct, IEEE Xplore, ACM, and MDPI), using search strings to identify papers that are in the scope of this review. Finally, 45 papers were included in the analysis, the first being published in 2015, which indicates an emerging area. Among the gaps found, we can mention the need for better clinical interpretability of the results obtained in the papers, that is not to restrict the results or conclusions simply to performance metrics. In addition, a possible research direction is the use of new transforms. It is also important to make new public datasets available that can be used to train the models. [ABSTRACT FROM AUTHOR]

This paper combines the digital twin system modeling method to conduct an in-depth study and analysis of graph-theoretic combinatorial optimization. This paper provides new ideas and approaches for optimal numerical analysis work by studying the digital twin modeling method that integrates digital modeling and graph theory combination, provides theoretical support for safe, stable, and economic operation of the system, proposes a solution for digital twin model based on big data platform, focuses on the nearest neighbor propagation (AP) and graph theory combination, solves the digital twin real-time monitoring data asynchronous, incomplete problem, and applies the algorithm to the digital twin model based on the big data platform for data preprocessing to achieve better results. This paper also presents a web-based digital twin system based on intelligent practical needs, analysis, and comparison of existing models, combined with digital twin technology, detailing the differences and connections between the various levels of numerical analysis and the implementation of this data in various fields, such as user management, equipment health management, product quality management, and workshop 3D navigation and detailed modeling of the digital twin system based on this numerical analysis to realize remote online monitoring, analysis, and management. In this paper, for the numerical analysis process, firstly, the key technologies of modeling and simulation operation control of production line based on digital twin are studied, and the rapid response manufacturing system based on a digital twin is designed and validated. Secondly, a scheduling technology framework for capacity simulation evaluation and optimization is established, and batching optimization, outsourcing decision, and rolling scheduling techniques are thus proposed to form a batching optimization algorithm based on priority rules, which realizes batching processing, outsourcing decision, and rolling scheduling of production orders to optimize equipment utilization and capacity. Finally, digital twin-based modeling is designed, and the validation results demonstrate the system's superior performance in achieving information interaction between physical and virtual production lines, optimization of numerical analysis, and display of results. [ABSTRACT FROM AUTHOR]

With the increasing complexity of integrated circuit design, the threat of a hardware Trojan (HT) is becoming more and more prominent. At present, the research mainly focuses on the detection of HTs, but the amount of research on the diagnosis of HTs is very small. The number of existing HT diagnosis methods is generally completed by detecting the HT nodes in the netlist. The main reason is the lack of consideration of the integrity of HTs, so the diagnosis accuracy is low. Based on the above reason, this paper proposes two implanted node search algorithms named layer-by-layer difference search (LDS) and layer-by-layer grouping difference search (LGDS). The LDS algorithm can greatly reduce the search time, and the LGDS algorithm can solve the problem of input node disorder. The two methods greatly reduce the number of nodes sorting and comparing, and therefore the time complexity is lower. Moreover, the relevance between implanted nodes is taken into account to improve the diagnosis rate. We completed experiments on an HT diagnosis; the HT implantation example is from Trust-Hub. The experimental results are shown as follows: (1) The average true positive rate (TPR) of the diagnosis using KNN, RF, or SVM with the LDS or LGDS algorithm is more than 93%, and the average true negative rate (TNR) is 100%. (2) The average proportion of implanted nodes obtained by the LDS or LGDS algorithm is more than 97%. The proposed method has a lower time complexity compared with other existing diagnosis methods, and the diagnosis time is shortened by nearly 75%. [ABSTRACT FROM AUTHOR]

The scientific and reasonable division of geographical units of cultivated land reserve resource areas is an important foundation for comprehensive land consolidation (CLC). Saline–alkali land is an important cultivated land reserve resource, and is significant for ensuring food security. This paper constructs a two-level land consolidation index system for cultivated land reserve resource areas. The Kruskal graph theory clustering algorithm was used to divide the study area into four types of ecological zones. On the basis of ecological zones, the study area was further divided into three types of consolidation units. Finally, the spatial relationship between ecological zoning and land use types was clarified, and the classification distribution of land consolidation potential was determined through an analysis of the CLC of two-level geographical units. Da'an City, Jilin province, China, was selected as the study area. The results of this study show the following: (1) In Da'an City, the conservation priority areas are concentrated in the north, the development priority areas are concentrated in the central and southern areas, and the comprehensive upgrade areas and adjustment rebuilding areas are in the transition zones. (2) The CLC potential trend is low in the north but high in the south in Da'an City. This paper proposes a framework for a geographical unit delineation method for saline–alkali-enriched cultivated land reserve resource zones, and analyzes the spatial layout of ecological protection demands and land consolidation potential in Da'an City. The results and conclusions of this study will provide a reference for CLC in cultivated land reserve resource areas. [ABSTRACT FROM AUTHOR]

Failure of vulnerable lines in the power system often results in tidal shifts, and triggering chain failures and their corresponding transmission sections are concentrated manifestations of the weak links in the power system. It is very important to identify the vulnerable lines and search the transmission section to prevent the chain faults as well as to analyze the stability of the power system. Aiming at the problems of inaccurate search of vulnerable lines, difficulties adapting to the complex and changing power system as well as wrong selection and omission of transmission section search in the existing references, this paper proposes an algorithm for searching vulnerable lines and their key transmission sections based on the graph theory and PMU (phasor measurement unit) data. First, the method combines with the graph theory and PMU data to construct the grid topology map. Second, the comprehensive indicators for screening vulnerable lines are proposed by fully considering the network topology and line capacity, which combines with power exchange efficiency and energy fluctuation probability. Third, the distance matrix in the Floyd algorithm is transformed into a unit group that can store more elements, which reduces the traversal times of the algorithm and improves computational efficiency. The fast localization of transmission cross sections associated with vulnerable lines is realized. Finally, the critical transmission cross sections are screened according to the line outage distribution factor and line safety margin. The IEEE 39-bus system is selected for simulation experiments, and the simulation results show that the key transmission section search method proposed in this paper can better adapt to the variable power grid and is faster and more accurate than the other common method. [ABSTRACT FROM AUTHOR]

This paper extends the framework of soft set theory to directed graphs by introducing and analyzing the concepts of the normal product and restricted normal product of soft directed graphs. Building on Molodtsov’s foundational work in developing soft set theory to address uncertainty in data, this study presents new methods for modeling and understanding complex systems where uncertainty plays a significant role. Soft directed graphs, which enhance traditional graph models by incorporating parameters and uncertain relationships, serve as the foundation for this investigation. The normal product, defined as a combination of two soft directed graphs based on their respective parameter sets, and the restricted normal product, which combines soft directed graphs only where their parameter sets intersect, provide a comprehensive framework for these new operations. This paper also establishes the structural properties of these products, ensuring they are well-defined and retain the key features of soft directed graphs. Furthermore, we derive combinatorial identities related to vertex and arc counts, as well as degree sums, offering deeper insights into the composition and behavior of these graph products. [ABSTRACT FROM AUTHOR]

This paper delves into three research directions, leveraging the Lovász ϑ-function of a graph. First, it focuses on the Shannon capacity of graphs, providing new results that determine the capacity for two infinite subclasses of strongly regular graphs, and extending prior results. The second part explores cospectral and nonisomorphic graphs, drawing on a work by Berman and Hamud (2024), and it derives related properties of two types of joins of graphs. For every even integer such that n≥14, it is constructively proven that there exist connected, irregular, cospectral, and nonisomorphic graphs on n vertices, being jointly cospectral with respect to their adjacency, Laplacian, signless Laplacian, and normalized Laplacian matrices, while also sharing identical independence, clique, and chromatic numbers, but being distinguished by their Lovász ϑ-functions. The third part focuses on establishing bounds on graph invariants, particularly emphasizing strongly regular graphs and triangle-free graphs, and compares the tightness of these bounds to existing ones. The paper derives spectral upper and lower bounds on the vector and strict vector chromatic numbers of regular graphs, providing sufficient conditions for the attainability of these bounds. Exact closed-form expressions for the vector and strict vector chromatic numbers are derived for all strongly regular graphs and for all graphs that are vertex- and edge-transitive, demonstrating that these two types of chromatic numbers coincide for every such graph. This work resolves a query regarding the variant of the ϑ-function by Schrijver and the identical function by McEliece et al. (1978). It shows, by a counterexample, that the ϑ-function variant by Schrijver does not possess the property of the Lovász ϑ-function of forming an upper bound on the Shannon capacity of a graph. This research paper also serves as a tutorial of mutual interest in zero-error information theory and algebraic graph theory. [ABSTRACT FROM AUTHOR]

Recommender systems (RS) have been developed to make personalized suggestions and enrich users' preferences in various online applications to address the information explosion problems. However, traditional recommender-based systems act as black boxes, not presenting the user with insights into the system logic or reasons for recommendations. Recently, generating explainable recommendations with deep knowledge graphs (DKG) has attracted significant attention. DKG is a subset of explainable artificial intelligence (XAI) that utilizes the strengths of deep learning (DL) algorithms to learn, provide high-quality predictions, and complement the weaknesses of knowledge graphs (KGs) in the explainability of recommendations. DKG-based models can provide more meaningful, insightful, and trustworthy justifications for recommended items and alleviate the information explosion problems. Although several studies have been carried out on RS, only a few papers have been published on DKG-based methodologies, and a review in this new research direction is still insufficiently explored. To fill this literature gap, this paper uses a systematic literature review framework to survey the recently published papers from 2018 to 2022 in the landscape of DKG and XAI. We analyze how the methods produced in these papers extract essential information from graphbased representations to improve recommendations' accuracy, explainability, and reliability. From the perspective of the leveraged knowledge-graph related information and how the knowledge-graph or path embeddings are learned and integrated with the DL methods, we carefully select and classify these published works into four main categories: the Two-stage explainable learning methods, the Joint-stage explainable learning methods, the Path-embedding explainable learning methods, and the Propagation explainable learning methods. We further summarize these works according to the characteristics of the approaches and the recommendation scenarios to facilitate the ease of checking the literature. We finally conclude by discussing some open challenges left for future research in this vibrant field. [ABSTRACT FROM AUTHOR]

Deterministic transmission technology is a core key technology that supports deterministic real-time transmission requirements for industrial control in Time-Sensitive Networking (TSN). It requires each network node to have a deterministic forwarding delay to ensure the real-time end-to-end transmission of critical traffic streams. Therefore, when forwarding data frames, the switch nodes must consider the time-limited requirements of the traffic. In the input-queued switch system, an algorithm for clock-synchronized deterministic network traffic classification scheduling (CSDN-TCS) is proposed to address the issue of whether a higher-quality-of-service (QoS) performance can be provided under packet deadline constraints. First, the scheduling problem of the switch is transformed into a decomposition problem of the traffic matrix. Secondly, the maximum weight-matching algorithm in graph theory is used to solve the matching results slot by slot. By fully utilizing the slot resources, as many packets as possible can be scheduled to be completed before the deadline arrives. For two types of packet scheduling problems, this paper uses the maximum flow algorithm with upper- and lower-bound constraints to move packets from a larger deadline set to idle slots in a smaller deadline set, enabling early transmission, reducing the average packet delay, and increasing system throughput. When there are three or more types of deadlines in the scheduling set, this scheduling problem is an NP-hard problem. We solve this problem by polling the two types of scheduling algorithms. In this paper, simulation experiments based on the switching size and line load are designed, and the Earliest Deadline First (EDF) algorithm and the Flow-Based Iterative Packet Scheduling (FIPS) algorithm are compared with the CSDN-TCS algorithm. The simulation results show that under the same conditions, the CSDN-TCS algorithm proposed in this paper outperforms the other two algorithms in terms of success rate, packet loss rate, average delay and throughput rate. Compared with the FIPS algorithm, the CSDN-TCS algorithm has lower time complexity under the same QoS performance. [ABSTRACT FROM AUTHOR]

This paper formalizes the stepping stone problem introduced Ladoucer and Rebenstock [G] to the setting of simple graphs. This paper considers the set of functions from the vertices of our graph to N, which assign a fixed number of 1's to some vertices and assign higher numbers to other vertices by adding up their neighbors' assignments. The stepping stone solution is defined as an element obtained from the argmax of the maxima of these functions, and the maxima as its growth. This work is organized into work on the bounded and unbounded degree graph cases. In the bounded case, sufficient conditions are obtained for superlinear and sublinear stepping stone solution growth. Furthermore this paper demonstrates the existence of a basis of graphs which characterizes superlinear growth. In the unbounded case, properly sublinear and superlinear stepping stone solution growth are obtained. [ABSTRACT FROM AUTHOR]

This document discusses the importance of optimization in various fields such as statistics, biology, finance, economics, and control. It highlights the advancements made in optimization theory and methods, including first-order methods and augmented Lagrangian methods. The document also introduces a special issue on "Symmetry in Optimization Theory, Algorithms and Applications," which features five papers on topics such as ensemble learning, ant colony system algorithms, subspace algorithms, consensus problems in multi-agent systems, and dynamic conditional correlation models. The authors express their gratitude to the contributors and reviewers of the special issue. [Extracted from the article]

In this paper, a method of 3D concrete printing is used to find the optimal path of the nozzle running path. We propose a path optimization algorithm based on graph theory to solve two key problems in 3D concrete printing. The partitioning algorithm based on graph theory was adopted to improve the forming quality of concrete components, and ant colony algorithm was used to reduce printing time. The method was evaluated with 3D concrete printing experiments after introducing the process of implementing the partition algorithm and ant colony algorithm. The experiment results show a significant reduction in the idle strokes and the nozzle head-up times of the running path planned by the method in this paper. This has a direct impact on shortening the printing time and improving the forming quality. Compared with the other three conventional algorithms, the idle strokes of the nozzle planned by the method in this paper are reduced by 18.94%, 37.88%, and 66.67%, and the nozzle head-up times are reduced by 1.59%, 2.15%, and 8.69%. It provides a practical reference for the path optimization of 3D concrete printing. [ABSTRACT FROM AUTHOR]

"Multi-agent systems (MAS)" have been extensively studied across various fields, including robotics, economics, biology, and computer science. A distinctive feature of these systems is the ability of multiple agents, each with different characteristics, to perform system-wide tasks through local bottom-up interactions. Furthermore, design and control methods for system networks based on graph theory are being developed. Recent applications of these methods include autonomous driving technology, smart grids, and understanding social systems. This special issue aims to deepen the understanding of MAS, focusing on their control and applications. It features 16 papers, including one review paper. The accepted papers cover a wide range of topics, including reinforcement learning, autonomous mobility systems, and machine learning, presenting the latest research findings on MAS. These studies provide valuable insights into various aspects and potential applications of MAS. We hope that this issue will be beneficial to our readers and contribute to the advancement of future research. [ABSTRACT FROM AUTHOR]

This paper is concerned with the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. In contrast to existing synchronization network models, the current study considers both internal time‐varying delays and coupling time‐varying delays. By analyzing the two factors (i.e. time‐varying delays and uncertainties) on the synchronization performance of stochastic uncertain complex dynamic networks, a new inverse optimal adaptive control is proposed. The analysis tool developed in this paper is based on Lyapunov technique, algebraic graph theory and inverse optimality, which does not need to solve Hamilton‐Jacobi‐Bellman equation. Some sufficient conditions are established for the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. To demonstrate the effectiveness of the present approach, simulation results are illustrated. In this paper, we consider the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. Different from the existing synchronization of the networks model, we take the internal time‐varying delays and the coupling time‐varying delays into account. By analyzing the two factors (i.e. time‐varying delays and uncertainties) on the synchronization performance of stochastic uncertain complex dynamic networks, a novel inverse optimal adaptive control is proposed. The analysis tool developed in this paper is based on Lyapunov technique, algebraic graph theory and inverse optimality, which does not need to solve Hamilton‐Jacobi‐Bellman equation. Some sufficient conditions are established for the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. [ABSTRACT FROM AUTHOR]

Collaborative crowdsensing is a team collaboration model that harnesses the intelligence of a large network of participants, primarily applied in areas such as intelligent computing, federated learning, and blockchain. Unlike traditional crowdsensing, user recruitment in collaborative crowdsensing not only considers the individual capabilities of users but also emphasizes their collaborative abilities. In this context, this paper takes a unique approach by modeling user interactions as a graph, transforming the recruitment challenge into a graph theory problem. The methodology employs an enhanced Prim algorithm to identify optimal team members by finding the maximum spanning tree within the user interaction graph. After the recruitment, the collaborative crowdsensing explored in this paper presents a challenge of unfair incentives due to users engaging in free-riding behavior. To address these challenges, the paper introduces the MR-SVIM mechanism. Initially, the process begins with a Gaussian mixture model predicting the quality of users' tasks, combined with historical reputation values to calculate their direct reputation. Subsequently, to assess users' significance within the team, aggregation functions and the improved PageRank algorithm are employed for local and global influence evaluation, respectively. Indirect reputation is determined based on users' importance and similarity with interacting peers. Considering the comprehensive reputation value derived from the combined assessment of direct and indirect reputations, and integrating the collaborative capabilities among users, we have formulated a feature function for contribution. This function is applied within an enhanced Shapley value method to assess the relative contributions of each user, achieving a more equitable distribution of earnings. Finally, experiments conducted on real datasets validate the fairness of this mechanism. [ABSTRACT FROM AUTHOR]

This paper introduces a virtual consensus‐based wide area differential protection method through cooperative control concepts and graph theory. Using multi‐agent systems eliminates the need for a direct telecommunication connection between the protective relays to implement the proposed differential protection. In addition, applying telecommunication subgraphs facilitates the establishment of numerous differential protection areas. Collaboration between protected areas is facilitated by common agents, establishing a wide‐area cooperative protection network. The capability of the network operator to define various protection areas and the collaboration between these areas ensure the versatility of the proposed method for various protection purposes. The present paper primarily represents the application of the proposed protection system as a wide‐area supervisor protection for distance relays. Performance evaluations on an IEEE 39‐bus test system illustrate the method's effectiveness in various scenarios. The results show enhanced power system stability and resilience, particularly when traditional methods struggle to detect power swings with high impedance variation rates. [ABSTRACT FROM AUTHOR]

Background: The development of Brain-Computer Interface (BCI) technology has brought tremendous potential to various fields. In recent years, prominent research has focused on enhancing the accuracy of BCI decoding algorithms by effectively utilizing meaningful features extracted from electroencephalographic (EEG) signals. Objective: This paper proposes a method for extracting brain functional network features based on directed transfer function (DTF) and graph theory. The method incorporates the extracted brain network features with common spatial pattern (CSP) to enhance the performance of motor imagery (MI) classification task. Methods: The signals from each electrode of the EEG, utilizing a total of 32 channels, are used as input signals for the network nodes. In this study, 26 healthy participants were recruited to provide EEG data. The brain functional network is constructed in Alpha and Beta bands using the DTF method. The node degree (ND), clustering coefficient (CC), and global efficiency (GE) of the brain functional network are obtained using graph theory. The DTF network features and graph theory are combined with the traditional signal processing method, the CSP algorithm. The redundant network features are filtered out using the Lasso method, and finally, the fused features are classified using a support vector machine (SVM), culminating in a novel approach we have termed CDGL. Results: For Beta frequency band, with 8 electrodes, the proposed CDGL method achieved an accuracy of 89.13%, a sensitivity of 90.15%, and a specificity of 88.10%, which are 14.10, 16.69, and 11.50% percentage higher than the traditional CSP method (75.03, 73.46, and 76.60%), respectively. Furthermore, the results obtained with 8 channels were superior to those with 4 channels (82.31, 83.35, and 81.74%), and the result for the Beta frequency band were better than those for the Alpha frequency band (87.42, 87.48, and 87.36%). Similar results were also obtained on two public datasets, where the CDGL algorithm's performance was found to be optimal. Conclusion: The feature fusion of DTF network and graph theory features enhanced CSP algorithm's performance in MI task classification. Increasing the number of channels allows for more EEG signal feature information, enhancing the model's sensitivity and discriminative ability toward specific activities in brain regions. It should be noted that the functional brain network features in the Beta band exhibit superior performance improvement for the algorithm compared to those in the Alpha band. [ABSTRACT FROM AUTHOR]

Cubic fuzzy graphs (CFGs) offer greater utility as compared to interval-valued fuzzy graphs and fuzzy graphs due to their ability to represent the degree of membership for vertices and edges using both interval and fuzzy number forms. The significance of these concepts motivates us to analyze and interpret intricate networks, enabling more effective decision making and optimization in various domains, including transportation, social networks, trade networks, and communication systems. This paper introduces the concepts of vertex and edge connectivity in CFGs, along with discussions on partial cubic fuzzy cut nodes and partial cubic fuzzy edge cuts, and presents several related results with the help of some examples to enhance understanding. In addition, this paper introduces the idea of partial cubic α-strong and partial cubic δ-weak edges. An example is discussed to explain the motivation behind partial cubic α-strong edges. Moreover, it delves into the introduction of generalized vertex and edge connectivity in CFGs, along with generalized partial cubic fuzzy cut nodes and generalized partial cubic fuzzy edge cuts. Relevant results pertaining to these concepts are also discussed. As an application, the concept of generalized partial cubic fuzzy edge cuts is applied to identify regions that are most affected by trade deficits resulting from street crimes. Finally, the research findings are compared with the existing method to demonstrate their suitability and creativity. [ABSTRACT FROM AUTHOR]

Let G be a graph. For a set H of connected graphs, an H-factor of graph G is a spanning subgraph H of G such that every component of H is isomorphic to a member of H. Denote H = {P2}∪{Ci|i ≥ 3}. We call H-factor a perfect 2-matching of G, that is, a perfect 2-matching is a spanning subgraph of G such that each component of G is either an edge or a cycle. In this paper, we define the new concept of perfect 2-matching uniform graph, namely, a graph G is called a perfect 2-matching uniform graph if for arbitrary two distinct edges e1 and e2 of G, G contains a perfect 2-matching containing e1 and avoiding e2. In addition, we study the relationship between some graphic parameters and the existence of perfect 2-matching uniform graphs. The results obtained in this paper are sharp in some sense. [ABSTRACT FROM AUTHOR]

Stochastic complex networks with multi-weights which were driven by Brownian motion were widely investigated by many researchers. However, Brownian motion is not suitable for the modeling of engineering issues by reason of its variance, which is infinite at any time. So, in this paper, a novel kind of stochastic complex network with multi-weights driven by second-order process is developed. To disclose how the weights and second-order process affect the dynamical properties of stochastic complex networks with multi-weights driven by the second-order process, we discuss exponential stability of the system. Two types of sufficient criteria are provided to ascertain exponential stability of the system on the basis of Kirchhoff's matrix tree theorem and the Lyapunov method. Finally, some numerical examples are given to verify the correctness and validity of our results. [ABSTRACT FROM AUTHOR]

For the formation and obstacle avoidance challenges of UAVs (unmanned aerial vehicles) in complex scenarios, this paper proposes an improved collaborative strategy based on APF (artificial potential field). This strategy combines graph theory, the Leader–Follower method, and APF. Firstly, we used graph theory to design formation topology and dynamically adjust the distances between UAVs in real time. Secondly, we introduced APF to avoid obstacles in complicated environments. This algorithm innovatively integrates the Leader–Follower formation method. The design of this attractive field is replaced by the leader's attraction to the followers, overcoming the problem of unreachable targets in APF. Meanwhile, the introduced Leader–Follower mode reduces information exchange within the swarm, realizing a more efficient "few controlling many" paradigm. Afterwards, we incorporated rotational force to assist the swarm in breaking free from local minima. Ultimately, the stability of the integrated formation strategy was demonstrated using Lyapunov functions. The feasibility and effectiveness of the proposed strategy were validated across multiple platforms. [ABSTRACT FROM AUTHOR]

For the adjacency matrix A(G) and diagonal matrix of the vertex degrees D(G) of a simple graph G, the A(G) matrix is the convex combinations of D(G) and A(G), and is defined as A(G) = D(G)+(1)A(G), for 0 n be the eigenvalues of A(G) (which we call -adjacency eigenvalues of the graph G). The generalized adjacency energy also called -adjacency energy of the graph G is defined as EA (G) = is the average vertex degree, m is the size and n is the order of G. The -adjacency energy of a graph G merges the theory of energy (adjacency energy) and the signless Laplacian energy, as EA0 (G) = E (G) and 2E A 12 (G) = QE(G), where E (G) is the energy and QE(G) is the signless Laplacian energy of G. In this paper, we obtain some new upper and lower bounds for the generalized adjacency energy of a graph, in terms of different graph parameters like the vertex covering number, the Zagreb index, the number of edges, the number of vertices, etc. We characterize the extremal graphs attained these bounds. [ABSTRACT FROM AUTHOR]

With the rapid development of Open-Source (OS), more and more software projects are maintained and developed in the form of OS. These Open-Source projects depend on and influence each other, gradually forming a huge OS project network, namely an Open-Source Software ECOsystem (OSSECO). Unfortunately, not all OS projects in the open-source ecosystem can be healthy and stable in the long term, and more projects will go from active to inactive and gradually die. In a tightly connected ecosystem, the death of one project can potentially cause the collapse of the entire ecosystem network. How can we effectively prevent such situations from happening? In this paper, we first identify the basic project characteristics that affect the survival of OS projects at both project and ecosystem levels through the proportional hazards model. Then, we utilize graph convolutional networks based on the ecosystem network to extract the ecosystem environment characteristics of OS projects. Finally, we fuse basic project characteristics and environmental project characteristics and construct a Hybrid Structured Prediction Model (HSPM) to predict the OS project survival state. The experimental results show that HSPM significantly improved compared to the traditional prediction model. Our work can substantially assist OS project managers in maintaining their projects' health. It can also provide an essential reference for developers when choosing the right open-source project for their production activities. [ABSTRACT FROM AUTHOR]

Solving arithmetic word problems (AWPs) that involve deep implicit relations can be quite challenging. However, the paper proposed two approaches to tackle this issue. The first approach used the modifier-to-matrix (MTM) model to extract noun modification components from the problem text. Specifically, a missing entity recovery (MER) model translated explicit expressions into a node dependency graph (NDG). The nodes on the graph then recursively acquired connections from the knowledge base through the MER model until the goal was achieved with a known quantity. The solving engine then selected the appropriate knowledge as the prompt. The second approach proposed in the paper was a comprehensive one that combined explicit and implicit knowledge to enhance reasoning abilities. The experimental results of the dataset demonstrate that the proposed algorithm is superior to the baseline algorithms in solving AWPs that require deep implicit relations. [ABSTRACT FROM AUTHOR]

In order to take into account the influence of both system structure and diagnosis algorithm in the diagnosability design of the system, a diagnosability-integrated design method based on graph theory was proposed in this paper. Firstly, based on the diagnosability evaluation results, the difficulty of fault diagnosis was qualitatively analyzed using the K-means method, and the diagnosis plot of measurement point was drawn based on the analysis results. Secondly, the Bron–Kerbosch algorithm was used to extract the maximal cliques from the diagnosis plot of measurement point and determine the set of maximal cliques that can diagnose faults in the system based on the hypergraph edge coverage theorem. Finally, a cascade classifier was set on the maximal clique set to classify and identify faults in the system, and the performance of the diagnosis scheme was evaluated using the posterior probabilities of the classifier outputs combined with the Shannon entropy. At the same time, the method incorporated a measurement point update mechanism, which can decide whether to add additional measurement point according to the evaluation results of Shannon entropy to ensure better diagnosis effect. The results of simulation experiments showed that the fault diagnosis scheme designed by the method of this paper improved the correct rate of diagnosis results by 3.25 percentage points compared with other diagnosis schemes due to the simultaneous consideration of the structure of the system and the diagnosis method, and the diagnosis results of this paper were relatively stable in repeated experiments, which proved the practicality and effectiveness of the method of this paper. [ABSTRACT FROM AUTHOR]

Despite the huge advances in digital communications in the last decade, physical documents are still the most common media for information transfer, especially in the official context. However, the readily available document processing devices and techniques (printers, scanners, etc.) facilitate the illegal manipulation or imitation of original documents by forgers. Therefore, verification of the authenticity and detection of forgery is of paramount importance to all agencies receiving printed documents. We suggest an unsupervised forgery detection framework that can distinguish whether a document is forged based on the spectroscopy of the document's ink. The spectra of the tested documents inks (original and questioned) were obtained using laser-induced breakdown spectroscopy (LIBS) technology. Then, a correlation matrix of the spectra was calculated for both the original and questioned documents together, which were then transformed into an adjacency matrix aiming at converting it into a weighted network under the concept of graph theory. Clustering algorithms were then applied to the network to determine the number of clusters. The proposed approach was tested under a variety of scenarios and different types of printers (e.g., inkjet, laser, and photocopiers) as well as different kinds of papers. The findings show that the proposed approach provided a high rate of accuracy in identifying forged documents and a high detection speed. It also provides a visual output that is easily interpretable to the non-expert, which provides great flexibility for real-world application. [ABSTRACT FROM AUTHOR]

Locating transportation logistics centers (TLCs) is significant in organizing and easing the shipment of commodities. By choosing the right place and building a brand TLC, various producers and trade companies will benefit from its services. This paper applies the Euclidean theorem and graph theory to select an optimal place. Because the price of transportation services is an important challenge, this article shows ways to reduce it for the companies that are customers of the TLC. This study hypothesizes that a TLC network standardizes and improves services and reduces prices and after the building of Iranshahr's TLC, our aim is to synergize and connect it with a network of TLCs. Case studies were carried out on the building of a network of TLCs with four nodes in Coburg, Ashgabat, Iranshahr, and Chabahar. The novelty of this research is in the method used, which studies TLCs in two statuses—separately and with a network. The research includes, simultaneously, TLCs in both developed and developing economies with various socioeconomic formations. The paper analyses, methodologically, the economic behavior of the TLCs in the two situations using a mathematical model. The model uses two Lagrange target functions to prove that the network decreases prices while improving presented services. We found that multimodal cargo transportation by one TLC within a network of TLCs decreases the costs of transportation services and that the TLC network improved economies of scale through knowledge, technology, and experience synergy. The outcomes and model of this study will assist transportation planners and engineers in building and managing a TLC and including it in a network. [ABSTRACT FROM AUTHOR]

In 1975, Symons [[5]] introduced a subsemigroup of HT ht , defined as HT ht , for a nonempty subset I Y i of I X i , determining all its automorphisms. The first paper [[21]] introduces a construction of a new graph associated with a semihypergroup, using the fundamental relation HT ht . In particular, it is shown that the Cayley graphs generated by transposition trees on the set HT ht are HT ht -extendable and their extendability number is HT ht for any integer HT ht . Connections between algebraic structure theory and graph theory have been established in order to solve open problems in one theory with the help of the tools existing in the other, emphasizing the remarkable properties of one theory with techniques involving the second. [Extracted from the article]

Many properties of the structure and dynamics of complex networks derive from the characteristics of the spectrum of the associated Laplacian matrix, specifically from the set of its eigenvalues. In this paper, we show that there exist graphs for which the ratio between the length of the spectrum (that is, the difference between the largest and smallest eigenvalues of the Laplacian matrix) and its spread (the difference between the second smallest eigenvalue and the smallest one) is equal to the golden ratio. We call such graphs Golden Laplacian Graphs (GLG). In this paper, we first find all such graphs with a number of nodes n ≤ 10 . We then prove several graph-theoretic and algebraic properties that characterize these graphs. These graphs prove to be extremely robust, as they have large vertex and edge connectivity along with a large isoperimetric constant. Finally, we study the synchronization properties of GLGs, showing that they are among the top synchronizable graphs of the same size. Therefore, GLGs represent very good candidates for engineering and communication networks. [ABSTRACT FROM AUTHOR]

Spaceborne deployable cylindrical antennas have broad application prospects in the fields of space earth observation and remote-sensing detection because of their significant advantages of ultralong aperture, high gain, and flexible beam scanning. As application requirements rapidly develop, a new type of spaceborne deployable cylindrical antenna mechanism with a large diameter and deployability is urgently needed. This paper presents an innovative design for a cylindrical deployable antenna mechanism based on 18R triangular prism elements based on graph theory. The correctness of the configuration is verified by developing a prototype. First, four kinds of nonoverconstrained 12-bar triangular prism-stabilized truss structure configurations and their corresponding topological diagrams are constructed. Second, based on graph theory, three types of 102 triangular prism-stabilized truss mechanism configurations that can be folded into linear mechanisms are derived. Third, the kinematic pair configuration is established to achieve a single-degree-of-freedom 7R2U9S triangular prism deployable unit. Fourth, combined with the geometric topology characteristics of the unit network, a triangular prism unit networking method is proposed, and a cylindrical network mechanism configuration based on 18R triangular prism units is obtained. A prototype was fabricated by 3D printing, and an expansion and retraction function test was conducted, which verified the correctness of the theoretical analysis in this paper. Finally, a new concept configuration for a parabolic cylindrical antenna is proposed. This paper provides a reference for the configuration of large-scale folding truss structures with unit expansion. [ABSTRACT FROM AUTHOR]

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This is a noticeably short biography and introductory paper on multiplier Hopf algebras. It delves into questions regarding the significance of this abstract construction and the motivation behind its creation. It also concerns quantum linear groups, especially the coordinate ring of Mq(n) and the observation that K [Mq(n)] is a quadratic algebra, and can be equipped with a multiplier Hopf ∗-algebra structure in the sense of quantum permutation groups developed byWang and an observation by Rollier–Vaes. In our next paper, we will propose the study of multiplier Hopf graph algebras. The current paper can be viewed as a precursor to this upcoming work, serving as a crucial intermediary bridging the gap between the abstract concept of multiplier Hopf algebras and the well-developed field of graph theory, thereby establishing connections between them! This survey review paper is dedicated to the 78th birthday anniversary of Professor Alfons Van Daele. [ABSTRACT FROM AUTHOR]

Various methods are used when building bankruptcy prediction models. New sophisticated methods that are already used in other scientific fields can also be applied in this area. Graph theory provides a powerful framework for analyzing and visualizing complex systems, making it a valuable tool for assessing the sustainability and financial health of businesses. The motivation for the research was the interest in the application of this method rarely applied in predicting the bankruptcy of companies. The paper aims to propose an improved dynamic bankruptcy prediction model based on graph theoretical modelling. The dynamic model considering the causality relation between financial features was built for the period 2015–2021. Financial features entering the model were selected with the use of Domain knowledge approach. When building the model, the weights of partial permanents were proposed to determine their impact on the final permanent and the algorithm for the optimalisation of these weights was established to obtain the best performing model. The outcome of the paper is the improved dynamic graph theoretical model with a good classification accuracy. The developed model is applicable in the field of bankruptcy prediction and is an equivalent sophisticated alternative to already established models. [ABSTRACT FROM AUTHOR]

Advances in the development of collision-free path planning algorithms are the main need not only to solve mazes with robotic systems, but also for their use in modern product transportation or green logistics systems and planning merchandise deliveries inside or outside a factory. This challenge increases as the complexity of the task in its structure also increases. This paper deals with the development of a novel methodology for solving mazes with a mobile robot, using image processing techniques and graph theory. The novelty is that the mobile robot can find the shortest path from a start-point to the end-point into irregular mazes with abundant irregular obstacles, a situation that is not far from reality. Maze information is acquired from an image and depending on the size of the mobile robot, a grid of nodes with the same dimensions of the maze is built. Another contribution of this paper is that the size of the maze can be scaled from 1 m × 1 m to 66 m × 66 m, maintaining the essence of the proposed collision-free path planning methodology. Afterwards, graph theory is used to find the shortest path within the grid of reduced nodes due to the elimination of those nodes absorbed by the irregular obstacles. To avoid the mobile robot to travel through those nodes very close to obstacles and borders, resulting in a collision, each image of the obstacle and border is dilated taking into account the size of the mobile robot. The methodology was validated with two case studies with a mobile robot in different mazes. We emphasize that the maze solution is found in a single computational step, from the maze image as input until the generation of the Path vector. Experimental results show the usefulness of the proposed methodology, which can be used in applications such as intelligent traffic control, military, agriculture and so on. [ABSTRACT FROM AUTHOR]

Within the domain of robotic non-destructive testing (NDT) of complex structures, the existing methods typically utilise an offline robot-path-planning strategy. Commonly, for robotic inspection, this will involve full coverage of the component. An NDT probe oriented normal to the component surface is deployed in a raster scan pattern. Here, digital models are used, with the user decomposing complex structures into manageable scan path segments, while carefully avoiding obstacles and other geometric features. This is a manual process that requires a highly skilled robotic operator, often taking several hours or days to refine. This introduces several challenges to NDT, including the need for an accurate model of the component (which, for NDT inspection, is often not available), the requirement of skilled personnel, and careful consideration of both the NDT inspection method and the geometric structure of the component. This paper addresses the specific challenge of scanning complex surfaces by using an automated approach. An algorithm is presented, which is able to learn an efficient scan path by taking into account the dimensional constraints of the footprint of an ultrasonic phased-array probe (a common inspection method for NDT) and the surface geometry. The proposed solution harnesses a digital model of the component, which is decomposed into a series of connected nodes representing the NDT inspection points within the NDT process—this step utilises graph theory. The connections to other nodes are determined using nearest neighbour with KD-Tree optimisation to improve the efficiency of node traversal. This enables a trade-off between simplicity and efficiency. Next, movement restrictions are introduced to allow the robot to navigate the surface of a component in a three-dimensional space, defining obstacles as prohibited areas, explicitly. Our solution entails a two-stage planning process, as follows: a modified three-dimensional flood fill is combined with Dijkstra's shortest path algorithm. The process is repeated iteratively until the entire surface is covered. The efficiency of this proposed approach is evaluated through simulations. The technique presented in this paper provides an improved and automated method for NDT robotic inspection, reducing the requirement of skilled robotic path-planning personnel while ensuring full component coverage. [ABSTRACT FROM AUTHOR]

In this paper we investigate bottlenecks in adaptive dynamic surface control (DSC) and unveil an innovative consensus tracking controller to track the desired trajectory for a class of fractional-order multi-agent systems with non-linear dynamics. The study derives an algorithm by implementing graph theory and the DSC method. The main approaches in the control of fractional-order systems are the DSC and the adaptive DSC techniques to avoid the computational complexity of fractionalorder virtual control law. According to these techniques, a virtual control law is formulated and the proposed controller is passed through a fractional-order dynamic surface. By employing the DSC and adaptive DSC laws, we demonstrate that the desired consensus tracking between agents can be ensured. To verify the performance of the new approach, we simulate the desirable scenarios and evaluate the results against a popular adaptive sliding mode technique. [ABSTRACT FROM AUTHOR]

The volume of digital text data is continuously increasing both online and offline storage, which makes it difficult to read across documents on a particular topic and find the desired information within a possible available time. This necessitates the use of technique such as automatic text summarization. Many approaches and algorithms have been proposed for automatic text summarization including; supervised machine learning, clustering, graph-based and lexical chain, among others. This paper presents a novel systematic review of various graph-based automatic text summarization models. [ABSTRACT FROM AUTHOR]

Statistical characterizations of complex network structures can be obtained from both the Ihara Zeta function (in terms of prime cycle frequencies) and the partition function from statistical mechanics. However, these two representations are usually regarded as separate tools for network analysis, without exploiting the potential synergies between them. In this paper, we establish a link between the Ihara Zeta function from algebraic graph theory and the partition function from statistical mechanics, and exploit this relationship to obtain a deeper structural characterisation of network structure. Specifically, the relationship allows us to explore the connection between the microscopic structure and the macroscopic characterisation of a network. We derive thermodynamic quantities describing the network, such as entropy, and show how these are related to the frequencies of prime cycles of various lengths. In particular, the n-th order partial derivative of the Ihara Zeta function can be used to compute the number of prime cycles in a network, which in turn is related to the partition function of Bose–Einstein statistics. The corresponding derived entropy allows us to explore a phase transition in the network structure with critical points at high and low-temperature limits. Numerical experiments and empirical data are presented to evaluate the qualitative and quantitative performance of the resulting structural network characterisations. [ABSTRACT FROM AUTHOR]

In this paper, three sorts of network indices for the weighted three-layered graph are studied through the methods of graph spectra theory combined with analysis methods. The concept of union of graphs are applied to design two sorts of weighted layered multi-fan composed graphs, and the accurate mathematical expressions of the network indices are obtained through the derivations of Laplacian spectra; furthermore, the asymptotic properties are also derived. We find that when the cardinalities of the vertices on a sector-edge-link tend to infinity, the indices of FONC and EMFPT are irrelevant with the number of copies of the fan-substructure based on the considered graph framework. [ABSTRACT FROM AUTHOR]

In crisp graph theory, there are numerous topological indices accessible, including the Misbalance Prodeg Index, which is one of the most well-known degree-based topological indexes. In crisp graphs, both vertices and edges have membership values of 1 or 0, whereas in fuzzy graphs, both vertices and edges have different memberships. This is an entire contrast to the crisp graph. In this paper, we introduce the Fuzzy Misbalance Prodeg Index of a fuzzy graph, which is a generalized form of the Misbalance Prodeg Index of a graph. We find bounds of this index and find bounds of certain classes of graphs such as path graph, cycle graph, complete graph, complete bipartite graph, and star graph. We give an algorithm to find the Fuzzy Misbalance Prodeg Index of a graph for the model of multi-criteria decision-making is established. We present applications from daily life in multi-criteria decision-making. We apply our obtained model of the Fuzzy Misbalance Prodeg Index for the multicriteria decision-making to the choice of the best supplier and we also show the graphical analysis of our index with the other indices that show how our index is better than other existing indices. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of hesitant bipolar-valued fuzzy graph (HBVFG), which captures the two opposing perspectives, namely the positive and negative opinions. The novelty, importance and implications of this concept are illustrated by some results, examples, and graphical representations. There are, respectively, some theoretical terms of graphs such as partial directed hesitant bipolar-valued fuzzy subgraph (HBVFSG), directed HBVFSG, directed spanning HBVFSG, strong directed HBVFG and complete directed HBVFG which are introduced. The operations, such as Cartesian, direct, lexicographical, and strong products, are also defined between two HBVFGs with examples. The mapping relations, such as homomorphism, isomorphism, weak isomorphism, and co-weak isomorphism, are derived with an example. The applications of directed HBVFGs with algorithms for finding the optimal path in a network and the dominant node and influence of index with the self-persistence degree of a node in a social network are presented. For each problem, an algorithm is developed and its effectiveness is demonstrated by examples. The proposed concept is assessed in terms of theory and practice. The benefits of the proposed solution are highlighted and a clear comparison is made with the existing methods. [ABSTRACT FROM AUTHOR]

This research paper presents a methodology for improving wireless sensor network (WSN) performance by leveraging centrality measures, including degree, betweenness, closeness, eigenvector, and Katz centrality. Employing a random walk graph model, this study constructs networks with 30 and 50 nodes to investigate the impact of these centrality metrics on routing decisions to optimize energy efficiency, minimize latency, and enhance overall network reliability. Additionally, the paper provides a comprehensive analysis of the relationships among these centrality measures through various correlation techniques, such as Pearson correlation, Kendall rank correlation, and Spearman correlation, offering insights into how these metrics can effectively improve WSN operations. [ABSTRACT FROM AUTHOR]

Against the background of the construction of new power systems, power generation, transmission, distribution, and dispatching services are open to the outside world for interaction, and the accessibility of attack paths has been significantly enhanced. We are facing cyber-physical cross-domain attacks with the characteristics of strong targeting, high concealment, and cross-space threats. This paper proposes a quantitative analysis method for the influence of power cyber-physical cross-domain attack paths based on graph knowledge. First, a layered attack graph was constructed based on the cross-space and strong coupling characteristics of the power cyber-physical system business and the vertical architecture of network security protection focusing on border protection. The attack graph included cyber-physical cross-domain attacks, control master stations, measurement and control equipment failures, transient stable node disturbances, and other vertices, and achieved a comprehensive depiction of the attack path. Second, the out-degree, in-degree, vertex betweenness, etc., of each vertex in the attack graph were comprehensively considered to calculate the vertex vulnerability, and by defining the cyber-physical coupling degree and edge weights, the risk of each attack path was analyzed in detail. Finally, the IEEE RTS79 and RTS96 node systems were selected, and the impact of risk conduction on the cascading failures of the physical space system under typical attack paths was analyzed using examples, verifying the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]