Pentacyclic Harmonic Graph
Pure and Applied Mathematics Journal
Volume 5, Issue 5, October 2016, Pages: 165-173
Received: Aug. 28, 2016; Accepted: Sep. 8, 2016; Published: Oct. 11, 2016
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Authors
Ahmad Salehi Zarrin Ghabaei, Department of Mathematics, Parand Branch, Islamic Azad University, Parand, Iran
Shahroud Azami, Department of Mathematics, Parand Branch, Islamic Azad University, Parand, Iran
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Abstract
Let  be a graph on n vertices  and let  be the degree of vertex  A graph  is defined to be harmonic if  is an eigenvector of the -adjacency matrix of  We now show that there are 4 regular and 45 non-regular connected pentacyclic harmonic graphs and determine their structure. In the end we conclude that all of c-cyclic harmonic graphs for  are planar graphs.
Keywords
Harmonic Graph, Eigenvalue, Spectra
To cite this article
Ahmad Salehi Zarrin Ghabaei, Shahroud Azami, Pentacyclic Harmonic Graph, Pure and Applied Mathematics Journal. Vol. 5, No. 5, 2016, pp. 165-173. doi: 10.11648/j.pamj.20160505.15
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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