On the Harmonic Energy and Estrada index of Graphs

Abstract

Let G be a graph with n vertices and di is the degree of its i-th vertex( di is

the degree of vi), then the Harmonic matrix of G is the square matrix of order n

whose (i; j)-entry is equal to 2

di+dj

if the i-th and j-th vertex of G are adjacent,

and zero otherwise. The main purposes of this paper are to introduce the

Harmonic Estrada index of a graph. In addition we establish upper and lower

bounds for these energy and index separately also we investigate the relations

between the Harmonic Estrada index and the Harmonic energy.

Keywords

• Eigenvalue of graph,Energy,Harmonic Estrada index

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