Remarks on harmonic index of graphs

Abstract

The harmonic index of a connected graph G, denoted by H(G), is defined as H(G) = Σuv⋯2/d _u+d _v, where d _v is the degree of a vertex v in G. In this note, we extend a result of Zhong concerning the upper bound for harmonic index of unicyclic graphs to general connected graphs. In addition, we give a direct proof of Zhong's another result on the lower bound for harmonic index of trees.