Sum-Connectivity Coindex of Graphs under Operations

Abstract

Topological indices or coindices are mathematical parameters which are widely used to investigate different properties of graphs. The operations on graphs play vital roles in the formation of new molecular graphs from the old ones. Let $\mathrm{\Gamma }$ be a graph we perform four operations which are $S$ , $R$ , $Q,\text{\hspace{0.17em}and\hspace{0.17em}}T$ and obtained subdivisions type graphs such that $S\left(\mathrm{\Gamma }\right)$ , $R\left(\mathrm{\Gamma }\right)$ , $Q\left(\mathrm{\Gamma }\right)$ , and $T\left(\mathrm{\Gamma }\right)$ , respectively. Let ${\mathrm{\Gamma }}_1$ and ${\mathrm{\Gamma }}_2$ be two simple graphs; then, $F$ -sum graph is defined by performing the Cartesian product on $F\left({\mathrm{\Gamma }}_1\right)$ and ${\mathrm{\Gamma }}_2$ ; mathematically, it is denoted by ${\mathrm{\Gamma }}_{1+F}{\mathrm{\Gamma }}_2$ , where $F\in \left\{S,R,Q,T\right\}$ . In this article, we have calculated sum-connectivity coindex for $F$ -sum graphs. At the end, we have illustrated the results for particular $F$ -sum graphs with the help of a table consisting of numerical values.