点稳定子为Z4×Z2的8度1-正则Cayley图

doi:10.16088/j.issn.1001-6600.2015.01.010

广西师范大学学报（自然科学版） ›› 2015, Vol. 33 ›› Issue (1): 59-66.doi: 10.16088/j.issn.1001-6600.2015.01.010

点稳定子为Z₄×Z₂的8度1-正则Cayley图

徐尚进^1,2, 李平山^1,2, 黄海华^1,2, 李靖建^1,2

1. 广西大学数学与信息科学学院,广西南宁530004;
2. 广西高校数学及其应用重点实验室,广西南宁530004

收稿日期:2014-07-16 出版日期:2015-03-15 发布日期:2018-09-17
通讯作者: 徐尚进(1959—),男,安徽庐江人,广西大学教授,博士。E-mail:xusj@gxu.edu.cn
基金资助:
国家自然科学基金资助项目(10961004,11226141,11361006);广西自然科学基金资助项目(2013GXNSFAA019018;2013GXNSFBA019018;2012GXNSFBA053010);广西大学科研基金资助项目(XBZ110328)

8-Valent 1-Regular Cayley Graphs WhoseVertex Stabilizer is Z₄×Z₂

XU Shang-Jin^1,2, LI Ping-shan^1,2, HUANG Hai-hua^1,2, LI Jing-jian^1,2

1.College of Mathematices and Information Sciences, Guangxi University, Nanning Guangxi 530004, China;
2. Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, Nanning Guangxi 530004, China

Received:2014-07-16 Online:2015-03-15 Published:2018-09-17

摘要/Abstract

摘要： 一个图Γ称为1-正则图, 如果图Γ的图自同构群Aut(Γ)作用在它的弧集上正则. 本文给出了点稳定子为Z₄×Z₂的8度1-正则Cayley图的一个完全分类。

关键词: Cayley图, 1-正则, 无核

Abstract: A graph Γ is called 1-regular if its full automorphism group Aut(Γ) acts regularly on its arcs. In this paper, a complete characterization for 8-valent 1-regular Cayley Graphs with point stabilizer is presented. It is proved that there exists only 2 core-free 8-valent 1-regular Cayley graphs whose point stabilizer is Z₄×Z₂.

Key words: 1-regular, Cayley graph, core-free

中图分类号:

O157

徐尚进, 李平山, 黄海华, 李靖建. 点稳定子为Z₄×Z₂的8度1-正则Cayley图[J]. 广西师范大学学报（自然科学版）, 2015, 33(1): 59-66.

XU Shang-Jin, LI Ping-shan, HUANG Hai-hua, LI Jing-jian. 8-Valent 1-Regular Cayley Graphs WhoseVertex Stabilizer is Z₄×Z₂[J]. Journal of Guangxi Normal University(Natural Science Edition), 2015, 33(1): 59-66.

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点稳定子为Z₄×Z₂的8度1-正则Cayley图

8-Valent 1-Regular Cayley Graphs WhoseVertex Stabilizer is Z₄×Z₂

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