{"title":"关于 Cayley 和符号图-II","authors":"Deepakshi Sharma, Sachin Somra, Deepa Sinha","doi":"10.1007/s13370-024-01209-1","DOIUrl":null,"url":null,"abstract":"<div><p>The Cayley sum graph is a graph whose vertex comprises elements of an abelian group <i>G</i> and edges are the sum of these vertices belonging to a subset of <i>G</i>, namely, <i>S</i>. We introduce Cayley sum signed graph by giving the sign to these edges. An edge receives a positive sign if any of the incident vertices belong to <i>S</i>; otherwise, it receives a negative sign. We discuss the balance, clusterability and some properties of derived Cayley sum signed graph.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Cayley sum signed graphs-II\",\"authors\":\"Deepakshi Sharma, Sachin Somra, Deepa Sinha\",\"doi\":\"10.1007/s13370-024-01209-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The Cayley sum graph is a graph whose vertex comprises elements of an abelian group <i>G</i> and edges are the sum of these vertices belonging to a subset of <i>G</i>, namely, <i>S</i>. We introduce Cayley sum signed graph by giving the sign to these edges. An edge receives a positive sign if any of the incident vertices belong to <i>S</i>; otherwise, it receives a negative sign. We discuss the balance, clusterability and some properties of derived Cayley sum signed graph.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-024-01209-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-024-01209-1","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: 0
摘要
Cayley 和图是一种图，其顶点包含一个无常群 G 的元素，边是这些顶点属于 G 的一个子集（即 S）的和。如果任何一条边上的顶点都属于 S，那么这条边就会得到一个正号；否则，这条边就会得到一个负号。我们将讨论衍生 Cayley 和符号图的平衡性、可群集性和一些属性。
The Cayley sum graph is a graph whose vertex comprises elements of an abelian group G and edges are the sum of these vertices belonging to a subset of G, namely, S. We introduce Cayley sum signed graph by giving the sign to these edges. An edge receives a positive sign if any of the incident vertices belong to S; otherwise, it receives a negative sign. We discuss the balance, clusterability and some properties of derived Cayley sum signed graph.
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