双元 2-弧-直角双 Cayley 图形

Pub Date : 2024-03-02 DOI:10.1007/s10801-024-01297-z

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

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引用次数: 0

摘要

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

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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