{"title":"幂零图","authors":"D. Basnet, Ajay Sharma, Rahul Dutta","doi":"10.20429/tag.2021.080102","DOIUrl":null,"url":null,"abstract":"In this article, we introduce the concept of nilpotent graph of a finite commutative ring. The set of all non nilpotent elements of a ring is taken as the vertex set and two vertices are adjacent if and only if their sum is nilpotent. We discuss some graph theoretic properties of nilpotent graph.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Nilpotent Graph\",\"authors\":\"D. Basnet, Ajay Sharma, Rahul Dutta\",\"doi\":\"10.20429/tag.2021.080102\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we introduce the concept of nilpotent graph of a finite commutative ring. The set of all non nilpotent elements of a ring is taken as the vertex set and two vertices are adjacent if and only if their sum is nilpotent. We discuss some graph theoretic properties of nilpotent graph.\",\"PeriodicalId\":37096,\"journal\":{\"name\":\"Theory and Applications of Graphs\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-04-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory and Applications of Graphs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.20429/tag.2021.080102\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory and Applications of Graphs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.20429/tag.2021.080102","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
In this article, we introduce the concept of nilpotent graph of a finite commutative ring. The set of all non nilpotent elements of a ring is taken as the vertex set and two vertices are adjacent if and only if their sum is nilpotent. We discuss some graph theoretic properties of nilpotent graph.