On the general sum-connectivity index of tricyclic graphs

Abstract

The general sum-connectivity index of a graph G is a molecular descriptor defined as $$\chi _{\alpha }(G)=\sum _{uv\in E(G)}(d_G(u)+d_G(v))^\alpha $$ , where $$d_G(u)$$ denotes the degree of vertex u in G and $$\alpha $$ is a real number. In this paper, we obtain the first third graphs with maximum general sum-connectivity index among the connected tricyclic graphs of order n for $$\alpha \ge 1$$ by four transformations which increase the general sum-connectivity index.