The exact solutions of most nonlinear difference equations cannot be obtained theoretically sometimes. Therefore, a massive number of researchers predict the long behaviour of most difference equations by investigating some qualitative behaviours of these equations from the governing equations. In this article, we aim to analyze the asymptotic stability, global stability, periodicity of the solution of an eighth-order difference equation. Moreover, a theoretical solution of a special case equation will be presented in this paper.
Topological indices are real numbers associated with molecular graphs of compounds that help to guess properties of compounds. Hex-Derived networks has an assortment of valuable applications in drug store, hardware, and systems administration. Imran et al. [1] computed the general Randić, first Zagreb, ABC, GA, ABC\(_{4}\), and GA\(_{5}\) indices for these hex-derived networks. In this article, we extend the work of [1] and compute some new topological indices of these networks.
The mathematical chemistry deals with applications of graph theory to study the physicochemical properties of molecules theoretically. A chemical graph is a simple graph where hydrogen depleted atoms are vertices and covalent bonds between them represent the edges. A topological index of a graph is a numeric quantity obtained from the graph mathematically. A cactus graph is a connected graph in which no edges lie in more than one cycle. In this study, we derive exact expressions of general Zagreb index of some cactus chains.
In this paper, the covering radius of codes over \(\mathbb R ={\mathbb Z_2}{R^{*}},\) where \(R^{*}={\mathbb Z_2}+v{\mathbb Z_2},v^{2}=v\) with different weight are discussed. The block repetition codes over \(\mathbb R\) is defined and the covering radius for block repetition codes, simplex code of \(\alpha\)-type and \(\beta\)-type in \(\mathbb R\) are obtained.
