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.