Edge-transitive cubic graphs of twice square-free order

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-09-16 DOI:10.1002/jgt.23168

Gui Xian Liu, Zai Ping Lu

{"title":"Edge-transitive cubic graphs of twice square-free order","authors":"Gui Xian Liu, Zai Ping Lu","doi":"10.1002/jgt.23168","DOIUrl":null,"url":null,"abstract":"A graph is edge-transitive if its automorphism group acts transitively on the edge set. This paper presents a complete classification for connected edge-transitive cubic graphs of order <math>\n <semantics>\n <mrow>\n \n <mrow>\n <mn>2</mn>\n \n <mi>n</mi>\n </mrow>\n </mrow>\n <annotation> $2n$</annotation>\n </semantics></math>, where <math>\n <semantics>\n <mrow>\n \n <mrow>\n <mi>n</mi>\n </mrow>\n </mrow>\n <annotation> $n$</annotation>\n </semantics></math> is even and square-free. In particular, it is shown that such a graph is either symmetric or isomorphic to one of the following graphs: a semisymmetric graph of order 420, a semisymmetric graph of order 29,260, and five families of semisymmetric graphs constructed from the simple group <math>\n <semantics>\n <mrow>\n \n <mrow>\n <msub>\n <mtext>PSL</mtext>\n \n <mn>2</mn>\n </msub>\n \n <mrow>\n <mo>(</mo>\n \n <mi>p</mi>\n \n <mo>)</mo>\n </mrow>\n </mrow>\n </mrow>\n <annotation> ${{\\bf{\\text{PSL}}}}_{2}(p)$</annotation>\n </semantics></math>.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 1","pages":"173-204"},"PeriodicalIF":0.9000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Graph Theory","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23168","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

A graph is edge-transitive if its automorphism group acts transitively on the edge set. This paper presents a complete classification for connected edge-transitive cubic graphs of order $2 n$ , where $n$ is even and square-free. In particular, it is shown that such a graph is either symmetric or isomorphic to one of the following graphs: a semisymmetric graph of order 420, a semisymmetric graph of order 29,260, and five families of semisymmetric graphs constructed from the simple group ${PSL}_{2} (p)$ .

查看原文本刊更多论文

两倍无平方阶的边跨立方图

如果一个图的自变群在边集上作传递作用，那么这个图就是边传递图。本文介绍了阶为，其中阶为偶数且无平方的连边立方图的完整分类。本文特别指出，这样的图要么是对称的，要么与下列图同构：阶为 420 的半对称图、阶为 29 260 的半对称图，以及由简单群构造的五个半对称图族。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .