Bounds for the general sum-connectivity index of composite graphs

Abstract

The general sum-connectivity index is a molecular descriptor defined as χα(X)=∑xy∈E(X)(dX(x)+dX(y))α, where dX(x) denotes the degree of a vertex x∈ X, and α is a real number. Let X be a graph; then let R(X) be the graph obtained from X by adding a new vertex xe corresponding to each edge of X and joining xe to the end vertices of the corresponding edge e∈ E(X). In this paper we obtain the lower and upper bounds for the general sum-connectivity index of four types of graph operations involving R-graph. Additionally, we determine the bounds for the general sum-connectivity index of line graph L(X) and rooted product of graphs.