THE HARMONIC INDEX OF A GRAPH

摘要

The harmonic index of a graph G is defined asthesum of weights 2/d(v(i)) + d(v(j)) of all edges v(i)v(j) of G, whered d(vi) denotes the degree of the vertex v(n) in G. In this paper, we study how the harmonic index behaves when the graph is under perturbations.These results are used to provide a simpler method for determining the unicyclic graphs with maximum and minimum harmonic index among all unicyclic graphs, respectively. Moreover, alower bound for harmonic index is also obtained.