Abstract
The harmonic index of a graph G is defined as , where d(u) denotes the degree of a vertex u in G. It has been found that the harmonic index correlates well with the Randi c' index and with the π-electronic energy of benzenoid hydrocarbons. In this work, we give several relations between the harmonic index and diameter of graphs.
Highlights
All graphs considered in the following will be simple.Let G be a graph with vertex set V G and edge set E G
The order of graph G is the number of its vertices
Favaron et al [6] considered the relation between harmonic index and the eigenvalues of graphs
Summary
All graphs considered in the following will be simple.Let G be a graph with vertex set V G and edge set E G. The harmonic index of a graph is defined as uv E G Where d u denotes the degree of a vertex u in G . We give several relations between the harmonic index and diameter of graphs. Let G be a graph with vertex set V G and edge set E G .
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