{"title":"The Cayley sum graph of ideals of a semigroup","authors":"Afkhamizadeh Mojgan, Hassankhani Mehdi, Khashyarmanesh Kazem","doi":"10.56415/qrs.v30.01","DOIUrl":null,"url":null,"abstract":"Let S be a regular semigroup, I(S) be the set of ideals of S and M be a subset of I(S). In this paper, we introduce an undirected Cayley graph of S, denoted by Гs,m with elements of I(S) as the vertex set, and, for two distinct vertices I and J, I is adjacent to J if and only if there is an element K of M such that IK = J or JK = I. We study some basic properties of the graph Гs,m such as connectivity, girth and clique number. Moreover, we investigate the planarity, outerplanarity and ring graph of Гs,m.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v30.01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Let S be a regular semigroup, I(S) be the set of ideals of S and M be a subset of I(S). In this paper, we introduce an undirected Cayley graph of S, denoted by Гs,m with elements of I(S) as the vertex set, and, for two distinct vertices I and J, I is adjacent to J if and only if there is an element K of M such that IK = J or JK = I. We study some basic properties of the graph Гs,m such as connectivity, girth and clique number. Moreover, we investigate the planarity, outerplanarity and ring graph of Гs,m.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
