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Graph labeling allows for the representation of additional attributes or properties associated with the vertices, edges, or both of graphs. This can provide a more comprehensive and detailed representation of the system being modeled, allowing for a richer analysis and interpretation of the graph. Graph labeling in ladder graphs has a wide range of applications in engineering, computer science, physics, biology, and other fields. It can be applied to various problem domains, such as image processing, wireless sensor networks, VLSI design, bioinformatics, social network analysis, transportation networks, and many others. The versatility of ladder graphs and the ability to apply graph labeling to them make them a powerful tool for modeling and analyzing diverse systems. If a function Υ is an injective vertex assignment in {1,2,…q+1} and the inductive edge assignment function Υ* in {1,2,…q} is expressed as a graph with q edges, defined as Υ*(uv)=2[Υ(u)2+Υ(u)Υ(v)+Υ(v)2]3[Υ(u)+Υ(v)], then the function is referred to as F-centroidal mean labeling. This is known as the F-centroidal mean criterion. Here, we have determined the F-centroidal mean criteria of the graph ladder, slanting ladder, triangular ladder, TLn∘Sm, SLn∘Sm for m≤2, double-sided step ladder, Dn*, and diamond ladder.

This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for the stability of the proposed networks using the theory of discrete fractional calculus, the discrete Laplace transform, and the theory of fractional-order discrete Mittag–Leffler functions. In order to guarantee the global asymptotic stability, adequate criteria are determined using Lyapunov’s direct technique, the Lyapunov approach, and some novel analysis techniques of fractional calculation. Thus, some sufficient conditions are obtained to guarantee the global stability. The validity of the theoretical results are finally shown using numerical examples.

This article, we explore the stability analysis of stochastic fractional-order competitive neural networks with leakage delay. The main objective of this paper is to establish a new set of sufficient conditions, which is for the uniform stability in mean square of such stochastic fractional-order neural networks with leakage. Specifically, the presence and uniqueness of arrangements and stability in mean square for a class of stochastic fractional-order neural systems with delays are concentrated by using Cauchy-Schwartz inequality, Burkholder-Davis-Gundy inequality, Banach fixed point principle and stochastic analysis theory, respectively. Finally, four numerical recreations are given to confirm the hypothetical discoveries.

In this article synchronization of fractional order fuzzy BAM neural networks with time varying delays and reaction diffusion terms is studied. The time varying delays consist of discrete delays and distributed delays are considered. Then, some sufficient conditions black are presented to guarantee the global asymptotic stability of the error system by using Lyapunov-Krasovskii functional having the double integral terms, we utilized Jensens inequality techniques and LMI approach. Accordingly, we accomplished synchronization of master-slave fuzzy BAMNNs. The delay dependent stability conditions are set up in terms of linear matrix inequalities(LMIs), which can be productively understood utilizing Matlab LMI control tool box. At last, illustrative numerical results have been provided to verify the correctness and effectiveness of the obtained results.

In this paper, the synchronization of fractional-order uncertain delayed neural networks with an event-triggered communication scheme is investigated. By establishing a suitable Lyapunov–Krasovskii functional (LKF) and inequality techniques, sufficient conditions are obtained under which the delayed neural networks are stable. The criteria are given in terms of linear matrix inequalities (LMIs). Based on the drive–response concept, the LMI approach, and the Lyapunov stability theorem, a controller is derived to achieve the synchronization. Finally, numerical examples are presented to confirm the effectiveness of the main results.

This paper introduces a novel synchronization scheme for fractional-order neural networks with time delays and reaction-diffusion terms via pinning control. We consider Caputo fractional derivatives, constant delays and distributed delays in our model. Based on the stability behavior, fractional inequalities and Lyapunov-type functions, several criteria are derived, which ensure the achievement of a synchronization for the drive-response systems. The obtained criteria are easy to test and are in the format of inequalities between the system parameters. Finally, numerical examples are presented to illustrate the results. The obtained criteria in this paper consider the effect of time delays as well as the reaction-diffusion terms, which generalize and improve some existing results.

This paper investigates the global exponential stability of fractional order complex-valued neural networks with leakage delay and mixed time varying delays. By constructing a proper Lyapunov-functional we established sufficient conditions to ensure global exponential stability of the fractional order complex-valued neural networks. The stability conditions are established in terms of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

This paper is concerned with the problem of the robust stability of fractional-order memristive bidirectional associative memory (BAM) neural networks. Based on Lyapunov theory, fractional-order differential inequalities and linear matrix inequalities (LMI) are applied to obtain a robust asymptotical stability. Finally, numerical examples are presented.

This article examines the drive-response synchronization of a class of fractional order uncertain BAM (Bidirectional Associative Memory) competitive neural networks. By using the differential inclusions theory, and constructing a proper Lyapunov-Krasovskii functional, novel sufficient conditions are obtained to achieve global asymptotic stability of fractional order uncertain BAM competitive neural networks. This novel approach is based on the linear matrix inequality (LMI) technique and the derived conditions are easy to verify via the LMI toolbox. Moreover, numerical examples are presented to show the feasibility and effectiveness of the theoretical results.