{"title":"Graphical regular representations of (2,p)-generated groups","authors":"","doi":"10.1016/j.ejc.2024.104058","DOIUrl":null,"url":null,"abstract":"<div><p>For groups <span><math><mi>G</mi></math></span> 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 <span><math><mi>G</mi></math></span> to be a graphical regular representation (GRR), that is, for the Cayley graph to have full automorphism group isomorphic to <span><math><mi>G</mi></math></span>. This condition enables one to show the existence of GRRs of prescribed valency for a large class of groups, and in this paper, <span><math><mi>k</mi></math></span>-valent GRRs of finite nonabelian simple groups with <span><math><mrow><mi>k</mi><mo>≥</mo><mn>5</mn></mrow></math></span> are considered.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"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}
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Abstract
For groups 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 to be a graphical regular representation (GRR), that is, for the Cayley graph to have full automorphism group isomorphic to . This condition enables one to show the existence of GRRs of prescribed valency for a large class of groups, and in this paper, -valent GRRs of finite nonabelian simple groups with are considered.
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.
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