Cacti with maximal general sum-connectivity index

Abstract

Let V(G) and E(G) be, respectively, the vertex set and edge set of a graph G. The general sum-connectivity index of a graph G is denoted by $$\chi _\alpha (G)$$ and is defined as $$\sum \limits _{uv\in E(G)}(d_u+d_v)^\alpha $$ , where uv is an edge that connect the vertices $$u,v\in V(G)$$ , $$d_u$$ is the degree of a vertex u and $$\alpha $$ is any non-zero real number. A cactus is a graph in which any two cycles have at most one common vertex. Let $$\mathscr {C}_{n,t}$$ denote the class of all cacti with order n and t pendant vertices. In this paper, a maximum general sum-connectivity index ( $$\chi _\alpha (G)$$ , $$\alpha >1$$ ) of a cacti graph with order n and t pendant vertices is considered. We determine the maximum general sum-connectivity index of n-vertex cacti graph. Based on our obtained results, we characterize the cactus with a perfect matching having the maximum general sum-connectivity index.