关于基本 2 弧形传递图的分类结果

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-07-30 DOI:10.1016/j.disc.2024.114189

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引用次数: 0

摘要

如果一个连通图的全自形群有一个 2-arc-transitive 子群，并且它的每个最小正则子群在上最多有两个轨道，那么这个连通图就叫做基本 2-arc-transitive 图。1993 年，Praeger 证明了每一个有限 2-弧遍历连通图都是某个基本 2-弧遍历图的盖，并提出了有限基本 2-弧遍历图的分类问题。本文给出了阶为的基本 2-弧传递非双方图和阶为的基本 2-弧传递双方图的分类，其中和分别是不同的素数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A classification result about basic 2-arc-transitive graphs

A connected graph $Γ = (V, E)$ 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 $r^{a} s^{b}$ and basic 2-arc-transitive bipartite graphs of order $2 r^{a} s^{b}$ , where r and s are distinct primes.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

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.