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

Abstract

The harmonic index H(G) of a graph G is defined as the sum of the weights
of all edges uv of G, where d(u) denotes the degree of a vertex u in G. We give a best possible lower bound for the harmonic index of a graph (a triangle-free graph, respectively) with minimum degree at least two and characterize the extremal graphs.