{"title":"关于基本 2 弧形传递图的分类结果","authors":"","doi":"10.1016/j.disc.2024.114189","DOIUrl":null,"url":null,"abstract":"<div><p>A connected graph <span><math><mi>Γ</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> is called a basic 2-arc-transitive graph if its full automorphism group has a 2-arc-transitive subgroup <em>G</em>, and every minimal normal subgroup of <em>G</em> has at most two orbits on <em>V</em>. In 1993, Praeger proved that every finite 2-arc-transitive connected graph is a cover of some basic 2-arc-transitive graph, and proposed the classification problem of finite basic 2-arc-transitive graphs. In this paper, a classification is given for basic 2-arc-transitive non-bipartite graphs of order <span><math><msup><mrow><mi>r</mi></mrow><mrow><mi>a</mi></mrow></msup><msup><mrow><mi>s</mi></mrow><mrow><mi>b</mi></mrow></msup></math></span> and basic 2-arc-transitive bipartite graphs of order <span><math><mn>2</mn><msup><mrow><mi>r</mi></mrow><mrow><mi>a</mi></mrow></msup><msup><mrow><mi>s</mi></mrow><mrow><mi>b</mi></mrow></msup></math></span>, where <em>r</em> and <em>s</em> are distinct primes.</p></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A classification result about basic 2-arc-transitive graphs\",\"authors\":\"\",\"doi\":\"10.1016/j.disc.2024.114189\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A connected graph <span><math><mi>Γ</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> is called a basic 2-arc-transitive graph if its full automorphism group has a 2-arc-transitive subgroup <em>G</em>, and every minimal normal subgroup of <em>G</em> has at most two orbits on <em>V</em>. In 1993, Praeger proved that every finite 2-arc-transitive connected graph is a cover of some basic 2-arc-transitive graph, and proposed the classification problem of finite basic 2-arc-transitive graphs. In this paper, a classification is given for basic 2-arc-transitive non-bipartite graphs of order <span><math><msup><mrow><mi>r</mi></mrow><mrow><mi>a</mi></mrow></msup><msup><mrow><mi>s</mi></mrow><mrow><mi>b</mi></mrow></msup></math></span> and basic 2-arc-transitive bipartite graphs of order <span><math><mn>2</mn><msup><mrow><mi>r</mi></mrow><mrow><mi>a</mi></mrow></msup><msup><mrow><mi>s</mi></mrow><mrow><mi>b</mi></mrow></msup></math></span>, where <em>r</em> and <em>s</em> are distinct primes.</p></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X24003200\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24003200","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A classification result about basic 2-arc-transitive graphs
A connected graph is called a basic 2-arc-transitive graph if its full automorphism group has a 2-arc-transitive subgroup G, and every minimal normal subgroup of G has at most two orbits on V. In 1993, Praeger proved that every finite 2-arc-transitive connected graph is a cover of some basic 2-arc-transitive graph, and proposed the classification problem of finite basic 2-arc-transitive graphs. In this paper, a classification is given for basic 2-arc-transitive non-bipartite graphs of order and basic 2-arc-transitive bipartite graphs of order , where r and s are distinct primes.
期刊介绍:
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.