二面体群的交图

EIGEN MATHEMATICS JOURNAL Pub Date : 2021-12-30 DOI:10.29303/emj.v4i2.119

N. Nurhabibah, A. G. Syarifudin, I. G. A. W. Wardhana, Q. Aini

{"title":"二面体群的交图","authors":"N. Nurhabibah, A. G. Syarifudin, I. G. A. W. Wardhana, Q. Aini","doi":"10.29303/emj.v4i2.119","DOIUrl":null,"url":null,"abstract":"The intersection graph of a finite group G is a graph (V,E) where V is a set of all non-trivial subgroups of G and E is a set of edges where two distinct subgroups H_i , H_j are said to be adjacent if and only if H_i \\cap H_j \\neq {e} . This study discusses the intersection graph of a dihedral group D_{2n} specifically the subgraph, degree of vertices, radius, diameter, girth, and domination number. From this study, we obtained that if n=p^2 then the intersection graph of D_{2n} is containing complete subgraph K_{p+2} and \\gamma(\\Gamma_{D_{2n}})=p. ","PeriodicalId":281429,"journal":{"name":"EIGEN MATHEMATICS JOURNAL","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The Intersection Graph of a Dihedral Group\",\"authors\":\"N. Nurhabibah, A. G. Syarifudin, I. G. A. W. Wardhana, Q. Aini\",\"doi\":\"10.29303/emj.v4i2.119\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The intersection graph of a finite group G is a graph (V,E) where V is a set of all non-trivial subgroups of G and E is a set of edges where two distinct subgroups H_i , H_j are said to be adjacent if and only if H_i \\\\cap H_j \\\\neq {e} . This study discusses the intersection graph of a dihedral group D_{2n} specifically the subgraph, degree of vertices, radius, diameter, girth, and domination number. From this study, we obtained that if n=p^2 then the intersection graph of D_{2n} is containing complete subgraph K_{p+2} and \\\\gamma(\\\\Gamma_{D_{2n}})=p. \",\"PeriodicalId\":281429,\"journal\":{\"name\":\"EIGEN MATHEMATICS JOURNAL\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"EIGEN MATHEMATICS JOURNAL\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29303/emj.v4i2.119\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"EIGEN MATHEMATICS JOURNAL","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29303/emj.v4i2.119","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 2

摘要

有限群G的相交图是一个图(V,E)，其中V是G的所有非平凡子群的集合，E是两个不同子群H＿i, H＿j相邻的边的集合，当且仅当H＿i \cap H＿j \neq E{。本文讨论了二面体群}D＿2n{的交点图，特别是子图、顶点度、半径、直径、周长和支配数。通过研究，我们得到了当n=p^2时，}D＿2n{的相交图包含完全子图}K＿p+2{和}\gamma (\Gamma ＿D＿2n{)=p。{}}

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

The Intersection Graph of a Dihedral Group

The intersection graph of a finite group G is a graph (V,E) where V is a set of all non-trivial subgroups of G and E is a set of edges where two distinct subgroups H_i , H_j are said to be adjacent if and only if H_i \cap H_j \neq {e} . This study discusses the intersection graph of a dihedral group D_{2n} specifically the subgraph, degree of vertices, radius, diameter, girth, and domination number. From this study, we obtained that if n=p^2 then the intersection graph of D_{2n} is containing complete subgraph K_{p+2} and \gamma(\Gamma_{D_{2n}})=p.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

EIGEN MATHEMATICS JOURNAL

自引率

0.00%

发文量