Computing bounds for the general sum-connectivity index of some graph operations

Abstract

Let \(G\) be a graph with vertex set \(V(G)\) and edge set \(E(G)\). Denote by \(d_{G}(u)\) the degree of a vertex \(u\in V(G)\). The general sum-connectivity index of \(G\) is defined as \(\chi_{\alpha}(G)=\sum_{u_{1}u_2\in E(G)}(d_{G}(u_1)+d_{G}(u_2))^{\alpha}\), where \(\alpha\) is a real number. In this paper, we compute the bounds for general sum-connectivity index of several graph operations. These operations include corona product, cartesian product, strong product, composition, join, disjunction and symmetric difference of graphs. We apply the obtained results to find the bounds for the general sum-connectivity index of some graphs of general interest.