A lower bound for the harmonic index of a graph with minimum degree at least three

Abstract

The harmonic index H(G) of a graph G is the sum of the weights 2/d(u)+d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this work, a lower bound for the harmonic index of a graph with minimum degree at least three is obtained and the corresponding extremal graph is characterized.