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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]

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]

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]

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]

"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]

The second multiplicative Zagreb eccentricity index E*2 (G) of a simple connected graph G is expressed as the product of the weights ε(a)εG(b) over all edges ab of G, where ε(a) stands for the eccentricity of the vertex a in G. In this paper, some extremal problems on the E*2 index over some special graph classes including trees, unicyclic graphs and bicyclic graphs are examined, and the corresponding extremal graphs are characterized. Besides, the relationships between this vertex-eccentricity-based graph invariant and some well-known parameters of graphs and existing graph invariants such as the number of vertices, number of edges, minimum vertex degree, maximum vertex degree, eccentric connectivity index, connective eccentricity index, first multiplicative Zagreb eccentricity index and second multiplicative Zagreb index are investigated. [ABSTRACT FROM AUTHOR]

The Strip-Plot Design (SPD) is plays an important role in the complete block designs and also using the agricultural, medical and industry fields. SPD is best suited for a two-factor experiment that has more treatments than can be accommodated by a complete block design. In a SPD, one factor is assigned to the horizontal strip plot, one factor is assigned to the vertical - strip plot and one factor is interaction plot. Also, few experimental materials may be rare while other test items may be available in altering doses of other therapeutic factors, which may be expensive or time-consuming. One of the main features of SPD involves three types of experimental errors: row - strip plot error, coloum - strip plot error and interaction plot error. Experimenting across processing steps is essential for studying the interaction of factors where certain factors come from one step and others arrive from the other. The strip-plot design is a very efficient design for investigating multiple-step processes in terms of both resources and time. Strip-plot designs are economical when the factors are hard to change and the process under research has three discrete stages. When we want to study interactions between factors where some factors are from one step and other factors from another step, it is important to conduct experiments across processing steps. The approach is flexible because it can handle experimental design problems involving factors acting at different levels, unlike the existing method. Graphs are widely used representations of both natural and human-made structures. Graph theory can be used to investigate "things that are connected to other things. "Fits nearly everywhere. Some tough problems become easier to solve when they are represented graphically. We reviewed the agricultural field yield of the strip-plot design and early work on the design of industrial strip-plot design in this paper. We have also described the model of strip-plot design. We, therefore, advise experimenters to ensure that their strip-plot designs contain a sufficient number of rows and columns so that valid statistical inference is possible. A bipartite graph is one in which the edges can be divided into two sets without going into sets. A complete bipartite graph is a bipartite graph that is completed. The complete tripartite graph in which the edges can be divided into three set without going into sets. The cubic graph is a graph in which all vertices have degree three. This paper describes the construction and Statistical Analysis of SPD using some particular types of graphs is discussed through numerical examples. [ABSTRACT FROM AUTHOR]

This paper shows that there exist Reed-Solomon (RS) codes, over large finite fields, that are combinatorially list-decodable well beyond the Johnson radius, in fact almost achieving list-decoding capacity. In particular, we show that for any ε E (0,1] there exist RS codes with rate Ω(ε(log(1/∈)+1) that are list-decodable from radius of 1-ε. We generalize this result to list-recovery, showing that there exist (1-ε,l,O(l/ε)) -list-recoverable RS codes with rate Ω(εl√(log(1/ε)+1)) . Along the way we use our techniques to give a new proof of a result of Blackburn on optimal linear perfect hash matrices, and strengthen it to obtain a construction of strongly perfect hash matrices. To derive the results in this paper we show a surprising connection of the above problems to graph theory, and in particular to the tree packing theorem of Nash-Williams and Tutte. We also state a new conjecture that generalizes the tree-packing theorem to hypergraphs, and show that if this conjecture holds, then there would exist RS codes that are optimally (non-asymptotically) list-decodable. [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]

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]

With the growing size of online social communities, influence propagation in social networks has become a hot topic of the research. Most of the studies in this area are based on the assumption that the structure of the social network is static and does not change during the information spread process. However, real-world social networks are dynamic. Modeling this continuous dynamic behavior of social networks is a challenge that must be tackled. This paper proposes a hybrid Genetic Network Programming with Apriori algorithm (GNPA) for Influence Maximization (IM) in social networks. Proposed GNPA is a meta-heuristic based optimization algorithm that handles the dynamicity, i.e. user attribute values or connection between users that changes with time. The working of GNPA is divided into 5 steps. It begins with the identification of the initial population of seeds using discounted degree method. Next, it predicts the future changes using the Apriori algorithm and updates the network accordingly. After updating the network dynamics, the influence score is estimated using the local consistent Factorization machines for each edge of the network. Finally, the diffusion score of each individual of the population is calculated using a linear cascade model. After the completion of all the above steps, the population is updated by replacing the weak individuals with new individuals using mutation and crossover, which is the last step of GNPA. The efficacy of GNPA is evaluated over two real and two synthetic datasets with low out-degree ratio and high out-degree ratio. Experimental results demonstrated that GNPA is able to predict the changing behavior of the users close to the actual-time network and improved the influence propagation 16% to 38% as compared to the contemporary counterparts. [ABSTRACT FROM AUTHOR]

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The paper is devoted to two problems pivotal in the generation theory. The first concerns verifying whether a normalized holomorphic function is an infinitesimal generator. It is also important to trace the influence of properties of a generator on the dynamic behavior of the generated semigroup. Recently, these problems have been studied using the so-called filtrations of generators. In this paper we study three filtrations. The study of the first began earlier, the second is a new one, while the third consists of functions studied previously with no connection to complex dynamics. For all filtration classes studied in the paper, dynamic properties of the corresponding semigroups are established and estimates for the Fekete-Szegö functional are given. [ABSTRACT FROM AUTHOR]

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]

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]

Molodtsov’s introduction of soft set theory marked a significant advancement in managing uncertainty, addressing the limitations of classical set theory in handling imprecise and vague information. This versatile framework has since been extensively explored, leading to sophisticated models for decision-making and medical diagnosis. Building on the principles of soft set theory, the concept of soft graphs was introduced to enhance the representation and analysis of uncertain information. Soft graphs incorporate parametrization, enabling dynamic modeling of graph-based relationships across various contexts and applications. This innovative approach creates multiple, adaptable representations that better reflect real-world complexities. This survey paper provides a comprehensive guide to the evolution of soft graphs, starting with an overview of the origins and basic concepts of soft set theory, highlighting its strengths and applications. It then delves into the development of soft graphs, explaining their theoretical foundations and methodologies. The paper explores how soft graphs have been used to model and solve problems in different domains, emphasizing their flexibility and effectiveness. By examining both foundational concepts and contemporary research advancements, this paper serves as a valuable resource for researchers interested in the applications of soft set theory and soft graphs in managing uncertainty and imprecision. [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]

The Maximum Independent Set problem is well-studied in graph theory and related areas. An independent set of a graph is a subset of non-adjacent vertices of the graph. A maximum independent set is an independent set of maximum size. This paper studies the Maximum Independent Set problem in some classes of geometric intersection graphs in a distributed setting. More precisely, we study the Maximum Independent Set problem on two geometric intersection graphs, interval and axis-parallel segment intersection graphs, and present deterministic distributed algorithms in a model that is similar but a little weaker than the local communication model. We compute the maximum independent set on interval graphs in O(k) rounds and O(n) messages, where k is the size of the maximum independent set and n is the number of nodes in the graph. We provide a matching lower bound of Ω(k) on the number of rounds, whereas Ω(n) is a trivial lower bound on message complexity. Thus, our algorithm is both time and message-optimal. We also study the Maximum Independent Set problem in interval count l graphs, a special case of the interval graphs where the intervals have exactly l different lengths. We propose an 1 2-approximation algorithm that runs in O(l) round. For axis-parallel segment intersection graphs, we design an 1 2-approximation algorithm that obtains a solution in O(D) rounds. The results in this paper extend the results of Molla et al. [J. Parallel Distrib. Comput. 2019]. [ABSTRACT FROM AUTHOR]

Purpose: This paper presents the Edge Load Management and Optimization through Pseudoflow Prediction (ELMOPP) algorithm, which aims to solve problems detailed in previous algorithms; through machine learning with nested long short-term memory (NLSTM) modules and graph theory, the algorithm attempts to predict the near future using past data and traffic patterns to inform its real-time decisions and better mitigate traffic by predicting future traffic flow based on past flow and using those predictions to both maximize present traffic flow and decrease future traffic congestion. Design/methodology/approach: ELMOPP was tested against the ITLC and OAF traffic management algorithms using a simulation modeled after the one presented in the ITLC paper, a single-intersection simulation. Findings: The collected data supports the conclusion that ELMOPP statistically significantly outperforms both algorithms in throughput rate, a measure of how many vehicles are able to exit inroads every second. Originality/value: Furthermore, while ITLC and OAF require the use of GPS transponders and GPS, speed sensors and radio, respectively, ELMOPP only uses traffic light camera footage, something that is almost always readily available in contrast to GPS and speed sensors. [ABSTRACT FROM AUTHOR]

This paper presents a single tree segmentation method applied to 3D point cloud data acquired with a LiDAR scanner mounted on an unmanned aerial vehicle (UAV). The method itself is based on clustering methods and graph theory and uses only the spatial properties of points. Firstly, the point cloud is reduced to clusters with DBSCAN. Those clusters are connected to a 3D graph, and then graph partitioning and further refinements are applied to obtain the final segments. Multiple datasets were acquired for two test sites in the Czech Republic which are covered by commercial forest to evaluate the influence of laser scanning parameters and forest characteristics on segmentation results. The accuracy of segmentation was compared with manual labels collected on top of the orthophoto image and reached between 82 and 93% depending on the test site and laser scanning parameters. Additionally, an area-based approach was employed for validation using field-measured data, where the distribution of tree heights in plots was analyzed. [ABSTRACT FROM AUTHOR]

This paper proposes a computational method for the reliability of 2-separable networks. Based on graph theory and probability theory, this method simplifies the calculation process by constructing a network equivalent model and designing corresponding algorithms to achieve the efficient evaluation of reliability. Considering independent random failures of edges with equal probability q, this method can accurately calculate the reliability of 2-separable networks, and its effectiveness and accuracy are verified through examples. In addition, to demonstrate the generality of our method, we have also applied it to other 2-separable networks with fractal structures and proposed linear algorithms for calculating their all-terminal reliability. [ABSTRACT FROM AUTHOR]

This paper investigates the long-time behavior of fractional-order complex memristive neural networks in order to analyze the synchronization of both anatomical and functional brain networks, for predicting therapy response, and ensuring safe diagnostic and treatments of neurological disorder (such as epilepsy, Alzheimer's disease, or Parkinson's disease). A new mathematical brain connectivity model, taking into account the memory characteristics of neurons and their past history, the heterogeneity of brain tissue, and the local anisotropy of cell diffusion, is proposed. This developed model, which depends on topology, interactions, and local dynamics, is a set of coupled nonlinear Caputo fractional reaction–diffusion equations, in the shape of a fractional-order ODE coupled with a set of time fractional-order PDEs, interacting via an asymmetric complex network. In order to introduce into the model the connection structure between neurons (or brain regions), the graph theory, in which the discrete Laplacian matrix of the communication graph plays a fundamental role, is considered. The existence of an absorbing set in state spaces for system is discussed, and then the dissipative dynamics result, with absorbing sets, is proved. Finally, some Mittag–Leffler synchronization results are established for this complex memristive neural network under certain threshold values of coupling forces, memristive weight coefficients, and diffusion coefficients. [ABSTRACT FROM AUTHOR]

Metro network systems play an important role in urban transportation but they are vulnerable to various risks and disruptions. Having a comprehensive understanding of these risks is essential for their operation. In this paper, we aimed to assess the operational robustness of the Bucharest metro system. We employed graph theory and concepts. Using available data specific to the Bucharest metro system operation, we analyzed the type of disruptions across metro lines and stations. As expected, the two subway lines that sub-cross the city center experienced the greatest number of disruptions. Several stations on Line M1, that sub-cross the central urban area, were found to be particularly vulnerable. In our analysis, the results are as follows: the robustness indicator for the metro network, rT, is 0.1538, and the effective graph conductance (CG) is 0.1. These reveal that the Bucharest metro network can withstand up to 45% of node failures before collapsing. This indicates moderate robustness, suggesting that while the network can handle specific disruptions, targeted improvements are necessary to enhance overall resilience. [ABSTRACT FROM AUTHOR]

Fractional repetition codes (FRCs) are a special family of storage codes with the repair-by-transfer property in distributed storage systems. Constructions of FRCs are naturally related to combinatorial designs, graphs, and hypergraphs. In this paper, we consider an extremal problem on regular graphs related to FRCs where each packet is stored on ρ = 2 nodes. The problem asks for the minimum number of vertices in an α -regular graph such that any k vertices induce at most δ edges, where α , k, and δ are given. Such a problem is closely related to (and can be seen as a generalization of) the classical cage problem, and its solution indicates the minimum number of nodes in an FRC-based distributed storage system. In addition, we further consider FRCs with ρ ≥ 3 and generalize the extremal problem to a linear hypergraph version. [ABSTRACT FROM AUTHOR]

The main aim of the paper is to give the crossing number of the join product G* + Dn for the graph G* isomorphic to 4-regular graph on six vertices except for two distinct edges with no common vertex such that two remaining vertices are still adjacent, and where Dn consists of n isolated vertices. The proofs are done with possibility of an existence of a separating cycle in some particular drawing of the investigated graph G* and also with the help of well-known exact values for crossing numbers of join products of two subgraphs Hk of G* with discrete graphs. [ABSTRACT FROM AUTHOR]

Topological indices (TIs) have rich applications in various biological contexts, particularly in therapeutic strategies for cancer. Predicting the performance of compounds in the treatment of cancer is one such application, wherein TIs offer insights into the molecular structures and related properties of compounds. By examining, various compounds exhibit different degree-based TIs, analysts can pinpoint the treatments that are most efficient for specific types of cancer. This paper specifically delves into the topological indices (TIs) implementations in forecasting the biological and physical attributes of innovative compounds utilized in addressing cancer through therapeutic interventions. The analysis being conducted to derivatives of sulfonamides, namely, 4-[(2,4-dichlorophenylsulfonamido) methyl]cyclohexanecarboxylic acid (1), ethyl 4-[(naphthalene-2-sulfonamido) methyl]cyclohexanecarboxylate (2), ethyl 4-[(2,5-dichlorophenylsulfonamido) methyl]cyclohexanecarboxylate (3), 4-[(naphthalene-2-sulfonamido) methyl]cyclohexane-1-carboxylic acid (4) and (2S)-3-methyl-2-(naphthalene-1-sulfonamido)-butanoic acid (5), is performed by utilizing edge partitioning for the computation of degree-based graph descriptors. Subsequently, a linear regression-based model is established to forecast characteristics, like, melting point and formula weight in a quantitative structure-property relationship. The outcomes emphasize the effectiveness or capability of topological indices as a valuable asset for inventing and creating of compounds within the realm of cancer therapy. [ABSTRACT FROM AUTHOR]

Encryption and decryption are the two processes in the cryptosystem that ensure the safe transfer of data or sensitive information. Apart from classical mathematics, graph theory techniques are employed nowadays to construct a strong cryptosystem. This paper uses graph techniques such as decomposition and labelling to encrypt and decrypt an alphanumeric string of length 8. The novelty of this paper is the introduction of (S9,C3)-multi-decomposition and a new labelling technique - anti-magic decomposed labelling, which is applied in the cryptosystem. [ABSTRACT FROM AUTHOR]

This work introduces the development of path Dirac and hypergraph Dirac operators, along with an exploration of their persistence. These operators excel in distinguishing between harmonic and non-harmonic spectra, offering valuable insights into the subcomplexes within these structures. The paper showcases the functionality of these operators through a series of examples in various contexts. An essential facet of this research involves examining the operators' sensitivity to filtration, emphasizing their capacity to adapt to topological changes. The paper also explores a significant application of persistent path Dirac and persistent hypergraph Dirac in molecular science, specifically in analyzing molecular structures. The study introduces strict preorders derived from molecular structures, which generate graphs and digraphs with intricate path structures. The depth of information within these path complexes reflects the complexity of different preorder classes influenced by molecular structures. This characteristic underscores the effectiveness of these tools in the realm of topological data analysis. [ABSTRACT FROM AUTHOR]

There are many times when visuals and text will often disrupt each other in a single space and, as a result, make both more difficult to understand. Many methods exist to counteract this, such as placing text and visuals in specific locations in the given space. We have utilized these certain "combinations" to a great extent. Still, when there are special cases where these methods are less effective, finding an optimal combination as a replacement is more difficult. To see other patterns and techniques to assist in locating salient elements, we can use game theory and graph theory, as well as a small amount of cognitive neuroscience, to determine what combinations allow words and visuals to complement each other rather than compete. The research done in this paper is exemplified by bento grids, a recent design trend popularized by Apple. [ABSTRACT FROM AUTHOR]

In this paper, we discuss spectrum and energy of Arithmetic function signed graphs with respect to an arithmetical function and present some results. [ABSTRACT FROM AUTHOR]

A dissociation set of a graph G refers to a set of vertices inducing a subgraph with maximum degree at most 1 and serves as a generalization of two fundamental concepts in graph theory: Independent sets and induced matchings. The enumeration of specific substructures in grid graphs has been a captivating area of research in graph theory. Over the past few decades, the enumeration problems related to various structures in grid graphs such as Hamiltonian cycles, Hamiltonian paths, independent sets, maximal independent sets, and dominating sets have been deeply studied. In this paper, we enumerated dissociation sets in grid graphs using the state matrix recursion algorithm. [ABSTRACT FROM AUTHOR]