无核边缘传递的巢图

IF 0.6 3区数学 Q3 MATHEMATICS

Ars Mathematica Contemporanea Pub Date : 2023-09-15 DOI:10.26493/1855-3974.2944.9cd

István Kovács

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引用次数: 1

摘要

一个有限简单图Γ如果它是价为6的正则图，并且允许两个相同长度的轨道的自同构ρ，使得由这些轨道引起的子图中至少有一个是循环，则称为巢图。如果在Aut(Γ)中由ρ生成的群中没有非平凡子群是正常的，我们说Γ是无核的。本文证明，如果Γ是边传递且无核的，则它同构于下列图之一:Petersen图、Hamming图H(2,4)、Shrikhande图的补和k3,3的某法线2-覆盖。

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Edge-transitive core-free Nest graphs

A finite simple graph Γ is called a Nest graph if it is regular of valency 6 and admits an automorphism ρ with two orbits of the same length such that at least one of the subgraphs induced by these orbits is a cycle. We say that Γ is core-free if no non-trivial subgroup of the group generated by ρ is normal in Aut(Γ). In this paper, we show that, if Γ is edge-transitive and core-free, then it is isomorphic to one of the following graphs: the complement of the Petersen graph, the Hamming graph H(2,4), the Shrikhande graph and a certain normal 2-cover of K3, 3 by ℤ24.

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来源期刊

Ars Mathematica Contemporanea MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Ars mathematica contemporanea will publish high-quality articles in contemporary mathematics that arise from the discrete and concrete mathematics paradigm. It will favor themes that combine at least two different fields of mathematics. In particular, we welcome papers intersecting discrete mathematics with other branches of mathematics, such as algebra, geometry, topology, theoretical computer science, and combinatorics. The name of the journal was chosen carefully. Symmetry is certainly a theme that is quite welcome to the journal, as it is through symmetry that mathematics comes closest to art.