On the sum-connectivity index

Abstract

The sum-connectivity index of a simple graph G is defined in mathematical chemistry as R+(G) = ∑ uvєE(G)(du+dv)−1/2, where E(G) is the edge set of G and du is the degree of vertex u in G. We give a best possible lower bound for the sum-connectivity index of a graph (a triangle-free graph, respectively) with n vertices and minimum degree at least two and characterize the extremal graphs, where n ≥ 11.