Bounds for the general sum-connectivity index of composite graphs

Abstract The general sum-connectivity index is a molecular descriptor defined as χ α ( X ) = ∑ x y ∈ E ( X ) ( d X ( x ) + d X ( y ) ) α $\chi_{\alpha}(X)=\sum_{xy\in E(X)}(d_{X}(x)+d_{X}(y))^{\alpha}$ , where d X ( x ) $d_{X}(x)$ denotes the degree of a vertex x ∈ X $x\in X$ , and α is a real number. Let X be a graph; then let R ( X ) $R(X)$ be the graph obtained from X by adding a new vertex x e $x_{e}$ corresponding to each edge of X and joining x e $x_{e}$ to the end vertices of the corresponding edge e ∈ E ( X ) $e\in E(X)$ . 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 ) $L(X)$ and rooted product of graphs