{"title":"Bi-primitive 2-arc-transitive bi-Cayley graphs","authors":"Jing Jian Li, Xiao Qian Zhang, Jin-Xin Zhou","doi":"10.1007/s10801-024-01297-z","DOIUrl":null,"url":null,"abstract":"<p>A bipartite graph <span>\\(\\Gamma \\)</span> is a <i>bi-Cayley graph</i> over a group <i>H</i> if <span>\\(H\\leqslant \\textrm{Aut}\\Gamma \\)</span> acts regularly on each part of <span>\\(\\Gamma \\)</span>. A bi-Cayley graph <span>\\(\\Gamma \\)</span> is said to be a <i>normal bi-Cayley graph over H</i> if <span>\\(H\\unlhd \\textrm{Aut}\\Gamma \\)</span>, and <i>bi-primitive</i> if the bipartition preserving subgroup of <span>\\(\\textrm{Aut}\\Gamma \\)</span> acts primitively on each part of <span>\\(\\Gamma \\)</span>. In this paper, a classification is given for 2-arc-transitive bi-Cayley graphs which are bi-primitive and non-normal.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10801-024-01297-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
A bipartite graph \(\Gamma \) is a bi-Cayley graph over a group H if \(H\leqslant \textrm{Aut}\Gamma \) acts regularly on each part of \(\Gamma \). A bi-Cayley graph \(\Gamma \) is said to be a normal bi-Cayley graph over H if \(H\unlhd \textrm{Aut}\Gamma \), and bi-primitive if the bipartition preserving subgroup of \(\textrm{Aut}\Gamma \) acts primitively on each part of \(\Gamma \). In this paper, a classification is given for 2-arc-transitive bi-Cayley graphs which are bi-primitive and non-normal.
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