五价2正则无核Cayley图

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-03-17 DOI:10.1016/j.disc.2025.114479

Bo Ling, Zhi Ming Long

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引用次数: 0

摘要

如果Cayley图Γ=Cay（G，S）在某些X≤AutΓ上无核，则称其为2-正则无核，且AutΓ正则作用于Γ的2-弧集。本文对五价2正则无核Cayley图进行了分类。作为副产品，我们提供了Du等人（2017）[6]关于非阿贝尔简单群上的五价对称图的另一个结果的证明。即证明了非阿贝尔单群上的五价2正则Cayley图是正规的。进一步，我们构造了一个五价无核2-可传递的Cayley图Cay(G，S)，使得Aut（G，S）在S上可传递但不是2-可传递，这回答了Li在2008年提出的一个问题。

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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Pentavalent 2-regular core-free Cayley graphs

A Cayley graph

Γ = Cay (G, S)

is said to be 2-regular core-free if G is core-free in some

X ⩽ Aut Γ

and

Aut Γ

acts regularly on the set of 2-arcs of Γ. In this paper, we classify the pentavalent 2-regular core-free Cayley graphs. As a byproduct, we provide another proof of one of the results by Du et al. (2017) [6] regarding pentavalent symmetric graphs over non-abelian simple groups. Namely, we prove that the pentavalent 2-regular Cayley graphs over non-abelian simple groups are normal. Furthermore, we construct a pentavalent core-free 2-transitive Cayley graph

Cay (G, S)

such that

Aut (G, S)

is transitive but not 2-transitive on S. This answers a question posed by Li in 2008.

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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.