{"title":"价数为 6 的边先验图的完整分类","authors":"","doi":"10.1016/j.disc.2024.114205","DOIUrl":null,"url":null,"abstract":"<div><p>In 2020, the first author and Pan proved that every edge-primitive graph of valency 6 is 2-arc-transitive, and except the complete bipartite graph <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>6</mn><mo>,</mo><mn>6</mn></mrow></msub></math></span>, the automorphism group is almost simple, and they determined such graphs having a solvable edge stabilizer. The nonsolvable edge stabilizer case is settled in this work, which leads to a complete classification of edge-primitive graphs of valency 6.</p></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A complete classification of edge-primitive graphs of valency 6\",\"authors\":\"\",\"doi\":\"10.1016/j.disc.2024.114205\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In 2020, the first author and Pan proved that every edge-primitive graph of valency 6 is 2-arc-transitive, and except the complete bipartite graph <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>6</mn><mo>,</mo><mn>6</mn></mrow></msub></math></span>, the automorphism group is almost simple, and they determined such graphs having a solvable edge stabilizer. The nonsolvable edge stabilizer case is settled in this work, which leads to a complete classification of edge-primitive graphs of valency 6.</p></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-08-12\",\"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/S0012365X24003364\",\"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/S0012365X24003364","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A complete classification of edge-primitive graphs of valency 6
In 2020, the first author and Pan proved that every edge-primitive graph of valency 6 is 2-arc-transitive, and except the complete bipartite graph , the automorphism group is almost simple, and they determined such graphs having a solvable edge stabilizer. The nonsolvable edge stabilizer case is settled in this work, which leads to a complete classification of edge-primitive graphs of valency 6.
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.
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