{"title":"半群理想的Cayley和图","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":"{\"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}","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}
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.