Consensus of Delayed Fractional-Order Multiagent Systems Based on State-Derivative Feedback by Jun Liu, Kaiyu Qin, Wei Chen, Ping Li

“…A state-derivative feedback (SDF) is added into the designed control protocol in the existing paper to enhance the robustness of a fractional-order multiagent system (FMS) against nonuniform time delays in this paper. By applying the graph theory and the frequency-domain analysis theory, consensus conditions are derived to make the delayed FMS based on state-derivative feedback reach consensus. …”
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A Q-Learning-Based Parameters Adaptive Algorithm for Formation Tracking Control of Multi-Mobile Robot Systems by Chen Zhang, Wen Qin, Ming-Can Fan, Ting Wang, Mou-Quan Shen

“…Furthermore, the stability of the closed-loop control system is rigorously proved by means of matrix properties of graph theory and Lyapunov theory, and the formation tracking errors can be guaranteed to be uniformly ultimately bounded. …”
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THE MAMMALIAN CIRCADIAN CLOCK: GENE REGULATORY NETWORK AND THEIR COMPUTER ANALYSIS by O. A. Podkolodnaya, N. N. Podkolodnaya, N. L. Podkolodnyy

“…This paper presents the results of the reconstruction and analysis of gene regulatory network of the circadian clock in mammals. Application of graph theory methods makes it possible to analyze the structure of the gene network and identify the central component of circadian clock regulation, which includes the basic regulatory circuits passing through the key element of the circadian clock, the Clock/Bmal1 protein. …”
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Molecular Descriptors on Line Graphs of Cactus Chains and Rooted Products Graphs by Iftikhar Ahmad, Maqbool Ahmad Chaudhry, Tarkan Öner, Tariq Mahmood, Muhammad Hussain

“…The application of graph theory in the study of molecular physical and chemical properties involves theoretical mathematical chemistry. …”
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Multivalued Fixed Point Results for Two Families of Mappings in Modular-Like Metric Spaces with Applications by Tahair Rasham, Abdullah Shoaib, Choonkil Park, Manuel de la Sen, Hassen Aydi, Jung Rye Lee

“…Some new results in graph theory for multigraph-dominated contractions in modular-like metric spaces are developed. …”
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Eigenvalues of Relatively Prime Graphs Connected with Finite Quasigroups by Muhammad Nadeem, Nwazish Ali, Hafiz Muhammad Bilal, Md. Ashraful Alam, M. I. Elashiry, Kholood Alnefaie

“…A relatively new and rapidly expanding area of mathematics research is the study of graphs’ spectral properties. Spectral graph theory plays a very important role in understanding certifiable applications such as cryptography, combinatorial design, and coding theory. …”
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A New Type-2 Soft Set: Type-2 Soft Graphs and Their Applications by Khizar Hayat, Muhammad Irfan Ali, Bing-Yuan Cao, Xiao-Peng Yang

“…In this study, we present an application of type-2 soft sets in graph theory. We introduce vertex-neighbors based type-2 soft sets over X (set of all vertices of a graph) and E (set of all edges of a graph). …”
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A workflow for processing global datasets: application to intercropping by Mahmoud, Rémi, Casadebaig, Pierre, Hilgert, Nadine, Gaudio, Noémie

“…We developed a method to identify complete factorial designs within global datasets using tools from graph theory. We discuss the position of global datasets in the continuum between data and knowledge, compared to other approaches such as meta-analysis. …”
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Numerical and Scientific Investigation of Some Molecular Structures Based on the Criterion of Super Classical Average Assignments by A. Rajesh Kannan, Nazek Alessa, K. Loganathan, Balachandra Pattanaik

“…Numerous graph assignment techniques, including distance-based labeling, topological indices, and spectral graph theory, can be used to investigate molecule structures. …”
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Connection Number- Based Topological Indices of Cartesian Product of Graphs by Aiman Arshad, Aqsa Sattar, Muhammad Javaid, Mamo Abebe Ashebo

“…The area of graph theory (GT) is rapidly expanding and playing a significant role in cheminformatics, mostly in mathematics and chemistry to develop different physicochemical, chemical structure, and their properties. …”
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Distributed Robust Cooperative Hierarchical Control for Island Microgrids under Hijacking Attacks Based on Multiagent Systems by Abdollah Mirzabeigi, Ali Kazemy, Mehdi Ramezani, Seyed Mohammad Azimi

“…In this article, island microgrid has been investigated from the view of multiagent systems and graph theory. This study uses the cooperative distributed hierarchical controller in two primary and secondary layers to control the hijacking cyber-attack in the islanded microgrid. …”
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Evaluation of Bus Networks in China: From Topology and Transfer Perspectives by Hui Zhang, Peng Zhao, Yinhai Wang, Xiangming Yao, Chengxiang Zhuge

“…Some static properties based on graph theory and complex theory are used to evaluate bus topological structure. …”
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On Topological Analysis of Niobium (II) Oxide Network via Curve Fitting and Entropy Measures by Muhammad Kamran Siddiqui, Sana Javed, Sadia Khalid, Mazhar Hussain, Muhammad Shahbaz, Samuel Asefa Fufa

“…A modern field of applied chemistry is chemical graph theory. With the use of combinatorial methods, such as vertex and edge partitions, we explore the connection between atoms and bonds. …”
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Applications of magnesium iodide structure via modified-polynomials by Haleemah Ghazwani, Muhammad Kamran Jamil, Ali Ahmad, Muhammad Azeem, Ali N. A. Koam

“…Abstract A relatively recent approach in molecular graph theory for analyzing chemical networks and structures is called a modified polynomial. …”
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Modified Zagreb Connection Indices for Benes Network and Related Classes by Wenhu Wang, Asma Nisar, Asfand Fahad, Muhammad Imran Qureshi, Abdu Alameri

“…The study of networks such as Butterfly networks, Benes networks, interconnection networks, David-derived networks through graph theoretical parameters is among the modern trends in the area of graph theory. Among these graph theoretical tools, the topological Indices TIs have been frequently used as graph invariants. …”
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Weighted Couple-Group Consensus Analysis of Heterogeneous Multiagent Systems with Cooperative-Competitive Interactions and Time Delays by Xingcheng Pu, Chaowen Xiong, Lianghao Ji, Longlong Zhao

“…A novel weighted couple-group consensus protocol based on cooperation and competition interaction is designed, which can relax the in-degree balance condition. By using graph theory, general Nyquist criterion and Gerschgorin disc theorem, the time delay upper limit that the system may allow is obtained. …”
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Multiagent Systems as an Approach to Building Fuzzy voter Communities using fuzzy languages by Milambu Belangany, Pierre Kasengadia Motumbe, Eugène Mbuyi Mukendi

“…Voters, represented as fuzzy agents, communicate using imprecise language to form communities based on shared linguistic terms. By leveraging graph theory, we construct a model of a fuzzy voting system where agents are linked based on the similarity of their fuzzy language. …”
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On the Constant Partition Dimension of Some Generalized Families of Toeplitz Graph by Ali N. A. Koam, Ali Ahmad, Maryam Salem Alatawi, Adnan Khalil, Muhammad Azeem

“…The use of graph theory is prevalent in the field of network design, whereby it finds utility in several domains such as the development of integrated circuits, communication networks, and transportation systems. …”
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Global dynamics of a general class of multi-group epidemic models with latency and relapse by Xiaomei Feng, Zhidong Teng, Fengqin Zhang

“….$ In particular, a matrix-theoretic method is used to provethe global stability of the disease-free equilibrium when $R_0\leq1,$while a new combinatorial identity (Theorem 3.3 in Shuai and vanden Driessche [29]) in graph theory is applied to provethe global stability of the endemic equilibrium when $R_0>1.…”
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Hosoya and Harary Polynomials of TOX(n),RTOX(n),TSL(n) and RTSL(n) by Lian Chen, Abid Mehboob, Haseeb Ahmad, Waqas Nazeer, Muhammad Hussain, M. Reza Farahani

“…In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. …”
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