{"title":"A NOTE ON THE COPRIME GRAPH OF A GROUP","authors":"H. Dorbidi","doi":"10.22108/IJGT.2016.9125","DOIUrl":null,"url":null,"abstract":"In this paper we study the coprime graph of a group G. The coprime graph of a group G, denoted by G, is a graph whose vertices are elements of G and two distinct vertices x and y are adjacent if and only if ( jxj;jyj) = 1. In this paper, we show that ( G) = !( G) : We classify all the groups which G is a complete r partite graph or a planar graph. Also we study the automorphism group of G.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"5 1","pages":"17-22"},"PeriodicalIF":0.7000,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/IJGT.2016.9125","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 15
Abstract
In this paper we study the coprime graph of a group G. The coprime graph of a group G, denoted by G, is a graph whose vertices are elements of G and two distinct vertices x and y are adjacent if and only if ( jxj;jyj) = 1. In this paper, we show that ( G) = !( G) : We classify all the groups which G is a complete r partite graph or a planar graph. Also we study the automorphism group of G.
期刊介绍：
International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.
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