Exact formulae of general sum-connectivity index for some graph operations

Abstract

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The degree of a vertex $a\in V(G)$ is denoted by $d_G(a)$. The general sum-connectivity index of $G$ is defined as ${\chi }_{\alpha }(G)=\sum _{ab\in E(G)}(d_G(a)+d_G(b){)}^{\alpha }$, where $\alpha$ is a real number. In this paper, we compute exact formulae for general sum-connectivity index of several graph operations. These operations include tensor product, union of graphs, splices and links of graphs and Haj\'{o}s construction of graphs. Moreover, we also compute exact formulae for general sum-connectivity index of some graph operations for positive integral values of $\alpha$. These operations include cartesian product, strong product, composition, join, disjunction and symmetric difference of graphs.