Bi-primitive 2-arc-transitive bi-Cayley graphs

IF 0.6 3区数学 Q3 MATHEMATICS Journal of Algebraic Combinatorics Pub Date : 2024-03-02 DOI:10.1007/s10801-024-01297-z

Jing Jian Li, Xiao Qian Zhang, Jin-Xin Zhou

引用次数: 0

Abstract

A bipartite graph $\Gamma $ is a bi-Cayley graph over a group H if $H\leqslant \textrm{Aut}\Gamma $ acts regularly on each part of $\Gamma $. A bi-Cayley graph $\Gamma $ is said to be a normal bi-Cayley graph over H if $H\unlhd \textrm{Aut}\Gamma $, and bi-primitive if the bipartition preserving subgroup of $\textrm{Aut}\Gamma $ acts primitively on each part of $\Gamma $. In this paper, a classification is given for 2-arc-transitive bi-Cayley graphs which are bi-primitive and non-normal.

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双元 2-弧-直角双 Cayley 图形

如果 $H\leqslant \textrm{Aut}\Gamma $有规律地作用于 $\Gamma $的每一部分，那么一个双分图 $\Gamma $就是一个在群 H 上的双凯利图。如果 $H\unlhd \textrm{Aut}\Gamma $的双分区保留子群原始地作用于 $\textrm{Aut}\Gamma $的每一部分，则称$\unlhd \textrm{Aut}\Gamma $为H上的正常双凯利图；如果 $\textrm{Aut}\Gamma $的双分区保留子群原始地作用于 $\textrm{Aut}\Gamma $的每一部分，则称$\unlhd \textrm{Aut}\Gamma $为H上的正常双凯利图。本文给出了双正则和非正则的 2-弧传递双凯利图的分类。

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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来源期刊

Journal of Algebraic Combinatorics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.

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