Dergiler / MATI / 2019 / Cilt: 1 - Sayı: 1

On the Harmonic Energy and Estrada index of Graphs

On the Harmonic Energy and Estrada index of Graphs

Akbar JAHANBANİ, Hassan HEKMATYAN RAZ

Dergi
MATI
Sayfa
1–20
DOI
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Abstract

Let G be a graph with n vertices and di is the degree of its i-th vertex( di isthe degree of vi), then the Harmonic matrix of G is the square matrix of order nwhose (i; j)-entry is equal to 2di+djif the i-th and j-th vertex of G are adjacent,and zero otherwise. The main purposes of this paper are to introduce theHarmonic Estrada index of a graph. In addition we establish upper and lowerbounds for these energy and index separately also we investigate the relationsbetween the Harmonic Estrada index and the Harmonic energy.