This analysis emphasizes the significance of radiation and chemical reaction effects on the boundary layer flow (BLF) of Casson liquid over a linearly elongating surface, as well as the properties of momentum, entropy production, species, and thermal dispersion. The mass diffusion coefficient and temperature-dependent models of thermal conductivity and species are used to provide thermal transportation. Nonlinear partial differential equations (NPDEs) that go against the conservation laws of mass, momentum, heat, and species transportation are the form arising problems take on. A set of coupled dimensionless partial differential equations (PDEs) are obtained from a set of convective differential equations by applying the proper non-similar transformations. Local non-similarity approaches provide an analytical approximation of the dimensionless non-similar system up to two degrees of truncations. The built-in Matlab (Version: 7.10.0.499 (R2010a)) solver bvp4c is used to perform numerical simulations of the local non-similar (LNS) truncations.

Circulant networks are a very important and widely studied class of graphs due to their interesting and diverse applications in networking, facility location problems, and their symmetric properties. The structure of the graph ensures that it is symmetric about any line that cuts the graph into two equal parts. Due to this symmetric behavior, the resolvability of these graph becomes interning. Subdividing an edge means inserting a new vertex on the edge that divides it into two edges. The subdivision graph G is a graph formed by a series of edge subdivisions. In a graph, a resolving set is a set that uniquely identifies each vertex of the graph by its distance from the other vertices. A metric basis is a resolving set of minimum cardinality, and the number of elements in the metric basis is referred to as the metric dimension. This paper determines the minimum resolving set for the graphs $H_l[1,k]$ constructed from the circulant graph $C_l[1,k]$ by subdividing its edges. We also proved that, for $k=2,3$, this graph class has a constant metric dimension.

This article addresses the problem of containment control of fractional-order multi-agent systems (FOMASs) subject to practical restrictions, such as actuator saturation, stochastic perturbations, and communication delays. A new delay-margin-based control framework is proposed to examine and improve the robustness and stability of containment strategies. To handle nonlinearities, stochastic effects, and time-varying delays, an adaptive control scheme is synthesized using the fractional-order system dynamics and observer-based compensation. The proposed control protocol guarantees the asymptotic convergence of follower agents to the convex hull generated by multiple leaders, regardless of actuator constraints and random disturbances. Saturation-aware compensation and stochastic modeling ensure resilience against adverse cyber-physical perturbations. Lyapunov-based fractional calculus techniques are used to analyze stability and convergence rigorously. Long simulation studies are provided to confirm the theoretical results and demonstrate the effectiveness and robustness of the proposed containment method under various uncertain scenarios.

Nanostar dendrimers are tree-like nanostructures with a well-defined, symmetrical architecture. They are built in a step-by-step, controlled synthesis process, with each layer or generation building on the previous one. Dendrimers are made up of a central core, a series of repeating units or branches, and a surface group shell. A weighted graph is a type of graph in which vertices or edges are assigned weights that represent cost, distance, and a variety of other relative measuring units. The weighted graphs have many applications and properties in a mathematical context. The topological indices are numerical values that represent the symmetry of a molecular structure. They have rich applications in theoretical chemistry. Various topological indices can be used to investigate a wide range of properties of chemical compounds with a molecular structure. They are very important in mathematical chemistry, especially in quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies. In this paper, we examine the topological properties of the molecular graphs of nanostar dendrimers. For this purpose, the topological indices, namely, the Wiener index and the Wiener polarity index are computed for a class of nanostar dendrimers.

In this article, our objective is to define and study a new subclass of analytic functions associated with the q-analogue of the sine function, operating in conjunction with a convolution operator. By manipulating the parameter q, we observe that the image of the unit disc under the q-sine function exhibits a visually appealing resemblance to a figure-eight shape that is symmetric about the real axis. Additionally, we investigate some important geometrical problems like necessary and sufficient conditions, coefficient bounds, Fekete-Szegö inequality, and partial sum results for the functions belonging to this newly defined subclass.

The generalized Petersen graphs are a type of cubic graph formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon. This graph has many interesting graph properties. As a result, it has been widely researched. In this work, the edge metric dimensions of the generalized Petersen graphs GP(2l + 1, l) and GP(2l, l) are explored, and it is shown that the edge metric dimension of GP(2l + 1, l) is equal to its metric dimension. Furthermore, it is proved that the upper bound of the edge metric dimension is the same as the value of the metric dimension for the graph GP(2l, l).