The harmonic index of bicyclic graphs with given matching number

Abstract

The harmonic index of a graph G is defined as the sum of weights 2/d(u)+d(v)of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, we determine the bicyclic graph with minimum harmonic index among all bicyclic graphs with a given size of matching. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.