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## On the Harmonic Energy and Estrada index of Graphs

#### Akbar JAHANBANİ  , Hassan HEKMATYAN RAZ 

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.

Eigenvalue of graph, Energy, Harmonic Estrada index
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Primary Language en Articles Author: Akbar JAHANBANİ (Primary Author)Institution: Department of Mathematics, Shahrood University of Technology, Shahrood, IranCountry: Iran Author: Hassan HEKMATYAN RAZ Institution: Department of Engineering, Yasuj Branch, Islamic Azad university, Yasuj, IranCountry: Iran Publication Date : January 2, 2019
 Bibtex @research article { mati425047, journal = {MATI}, issn = {2636-7785}, address = {}, publisher = {Süleyman EDİZ}, year = {2019}, volume = {1}, pages = {1 - 20}, doi = {}, title = {On the Harmonic Energy and Estrada index of Graphs}, key = {cite}, author = {Jahanbani̇, Akbar and Hekmatyan Raz, Hassan} } APA Jahanbani̇, A , Hekmatyan Raz, H . (2019). On the Harmonic Energy and Estrada index of Graphs . MATI , 1 (1) , 1-20 . Retrieved from https://dergipark.org.tr/en/pub/mati/issue/38227/425047 MLA Jahanbani̇, A , Hekmatyan Raz, H . "On the Harmonic Energy and Estrada index of Graphs" . MATI 1 (2019 ): 1-20 Chicago Jahanbani̇, A , Hekmatyan Raz, H . "On the Harmonic Energy and Estrada index of Graphs". MATI 1 (2019 ): 1-20 RIS TY - JOUR T1 - On the Harmonic Energy and Estrada index of Graphs AU - Akbar Jahanbani̇ , Hassan Hekmatyan Raz Y1 - 2019 PY - 2019 N1 - DO - T2 - MATI JF - Journal JO - JOR SP - 1 EP - 20 VL - 1 IS - 1 SN - 2636-7785- M3 - UR - Y2 - 2018 ER - EndNote %0 MATI On the Harmonic Energy and Estrada index of Graphs %A Akbar Jahanbani̇ , Hassan Hekmatyan Raz %T On the Harmonic Energy and Estrada index of Graphs %D 2019 %J MATI %P 2636-7785- %V 1 %N 1 %R %U ISNAD Jahanbani̇, Akbar , Hekmatyan Raz, Hassan . "On the Harmonic Energy and Estrada index of Graphs". MATI 1 / 1 (January 2019): 1-20 . AMA Jahanbani̇ A , Hekmatyan Raz H . On the Harmonic Energy and Estrada index of Graphs. Mati. 2019; 1(1): 1-20. Vancouver Jahanbani̇ A , Hekmatyan Raz H . On the Harmonic Energy and Estrada index of Graphs. MATI. 2019; 1(1): 1-20.

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