{"title":"Pentacyclic Harmonic Graph","authors":"Ahmad Salehi Zarrin Ghabaei, S. Azami","doi":"10.11648/J.PAMJ.20160505.15","DOIUrl":null,"url":null,"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.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"389 1","pages":"165"},"PeriodicalIF":0.2000,"publicationDate":"2016-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Italian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11648/J.PAMJ.20160505.15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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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.
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The “Italian Journal of Pure and Applied Mathematics” publishes original research works containing significant results in the field of pure and applied mathematics.
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