On the Harmonic Energy and Estrada index of Graphs

Year 2019, Volume: 1 Issue: 1, 1 - 20, 02.01.2019

Akbar Jahanbani , Hassan Hekmatyan Raz

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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