(2,p)生成群的图形正则表达式

IF 1 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2024-09-06 DOI:10.1016/j.ejc.2024.104058

Binzhou Xia

{"title":"(2,p)生成群的图形正则表达式","authors":"Binzhou Xia","doi":"10.1016/j.ejc.2024.104058","DOIUrl":null,"url":null,"abstract":"<div>For groups <math><mi>G</mi></math> that can be generated by an involution and an element of odd prime order, this paper gives a sufficient condition for a certain Cayley graph of <math><mi>G</mi></math> to be a graphical regular representation (GRR), that is, for the Cayley graph to have full automorphism group isomorphic to <math><mi>G</mi></math>. This condition enables one to show the existence of GRRs of prescribed valency for a large class of groups, and in this paper, <math><mi>k</mi></math>-valent GRRs of finite nonabelian simple groups with <math><mrow><mi>k</mi><mo>≥</mo><mn>5</mn></mrow></math> are considered.</div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"124 ","pages":"Article 104058"},"PeriodicalIF":1.0000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669824001434/pdfft?md5=c7da3e756f2ea49c07fc86ccf367f717&pid=1-s2.0-S0195669824001434-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Graphical regular representations of (2,p)-generated groups\",\"authors\":\"Binzhou Xia\",\"doi\":\"10.1016/j.ejc.2024.104058\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>For groups <math><mi>G</mi></math> that can be generated by an involution and an element of odd prime order, this paper gives a sufficient condition for a certain Cayley graph of <math><mi>G</mi></math> to be a graphical regular representation (GRR), that is, for the Cayley graph to have full automorphism group isomorphic to <math><mi>G</mi></math>. This condition enables one to show the existence of GRRs of prescribed valency for a large class of groups, and in this paper, <math><mi>k</mi></math>-valent GRRs of finite nonabelian simple groups with <math><mrow><mi>k</mi><mo>≥</mo><mn>5</mn></mrow></math> are considered.</div>\",\"PeriodicalId\":50490,\"journal\":{\"name\":\"European Journal of Combinatorics\",\"volume\":\"124 \",\"pages\":\"Article 104058\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0195669824001434/pdfft?md5=c7da3e756f2ea49c07fc86ccf367f717&pid=1-s2.0-S0195669824001434-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0195669824001434\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0195669824001434","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

对于可以由一个内卷和一个奇素数元素生成的群 G，本文给出了一个充分条件，即 G 的某个 Cayley 图是一个图形正则表达式（GRR），也就是 Cayley 图具有与 G 同构的全自形群。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Graphical regular representations of (2,p)-generated groups

For groups $G$ that can be generated by an involution and an element of odd prime order, this paper gives a sufficient condition for a certain Cayley graph of $G$ to be a graphical regular representation (GRR), that is, for the Cayley graph to have full automorphism group isomorphic to $G$ . This condition enables one to show the existence of GRRs of prescribed valency for a large class of groups, and in this paper, $k$ -valent GRRs of finite nonabelian simple groups with $k \geq 5$ are considered.

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

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.