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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]

In their work I "Fixed parameter algorithms for unsplittable flow cover i , Andrés Cristi, Mathieu Mari and Andreas Wiese considered UFP under the view point of parameterized complexity. The topics of the chosen papers cover various areas of Theoretical Computer Science, that is, algorithmic graph theory, automata theory, linear dynamical systems, parameterized complexity analysis, and distributed algorithms. This special issue contains 7 articles which are based on extended abstracts presented at the 36th I Symposium on Theoretical Aspects of Computer Science i (STACS). [Extracted from the article]

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]

Making grammars model makers as perceiving their environment and acting to transform it. Shape grammars, which model designers as manipulating shapes, are then a special case of making grammars where perceiving is limited to seeing and doing is limited to drawing. This paper develops set-theoretical and graph-theoretical formalizations of making grammars. Existing set-theoretical formalizations of shape grammars show that designing is visual computing by demonstrating that a shape grammar can be devised to simulate any Turing machine. However, there are no mathematical arguments showing how making grammars describe computation. Using a previously published example of a shape grammar and its corresponding making grammar, this paper combines ideas from ecological psychology with methods from set theory and graph theory to show that, for each Turing machine, a making grammar can be devised which simulates it. [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]

Formal Concept Analysis (FCA) is an applied branch of lattice theory, widely used in computer science that derives implicit relationships between objects described through a set of attributes on the one hand and these attributes on the other. Any finite lattice can be generated by a formal concept, which can be obtained from the formal context of objects and attributes. In this paper, given a finite lattice L with /(L)/ = /(L)/ = n where n is the number of atoms in the Boolean lattice Bn, we construct a formal context obtained by substitution sum ... and study the structural properties of the lattice BS(L) generated by the above substitution sum. Interestingly, the lattice L and the Boolean lattice Bn remain as separate entities in the lattice BS(L). Further, we have proved that the lattice BS(L) is complemented. [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]

In this paper, we apply the methods of graph theory to reveal hidden relations within the corpus of the Hebrew Bible texts. The structure of relations between different texts was studied based upon their interpretation of the otherworld and the afterlife. We have identified 43 most relevant texts that contained concepts related to the notion of the otherworld and constructed a graph representing the relations between the considered texts. The obtained graph was decomposed into 3 densely connected subgraphs using the Louvain method. An initial interpretation has been given to the results of the decomposition. Furthermore, we used different ranking methods to determine the most important texts forming the network structure of the intertextual connections. It turned out that there is an invariant set of texts that can be interpreted as having the larger influence or importance on the development of the idea of the otherworld. These texts are Proto-Isaiah, Qoheleth, Job, Psalms, and Proverbs as well as 1 Samuel, Ezekiel, and Book of Genesis. Furthermore, a detailed analysis of the notions, associated with these texts, reveals that there are several concepts that are likely to be associated with the most influential texts. [ABSTRACT FROM AUTHOR]