奇素数度的1-正则Cayley图

doi:10.16088/j.issn.1001-6600.2019.02.014

广西师范大学学报（自然科学版） ›› 2019, Vol. 37 ›› Issue (2): 121-125.doi: 10.16088/j.issn.1001-6600.2019.02.014

奇素数度的1-正则Cayley图

李靖建^1,2*, 朱文英¹, 解雅婷¹

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:2018-05-05 出版日期:2019-04-25 发布日期:2019-04-28
通讯作者: 李靖建(1976—), 男, 山东临沂人, 广西大学副教授, 博士。E-mail: lijjhx@163.com
基金资助:
国家自然科学基金(11461004);广西自然科学基金(2015GXNSFAA139001,2013GXNSFAA019018)

One-Regular Cayley Graphs of Valency Odd Prime

LI Jingjian^1,2*, ZHU Wenying¹, XIE Yating¹

1.School of Mathematics 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:2018-05-05 Online:2019-04-25 Published:2019-04-28

摘要/Abstract

摘要： 令Γ是一个图,如果Γ的自同构群Aut(Γ)作用在其弧集上是正则的,则称图Γ为1-正则图。在本文中,奇素数度1-正则Cayley图被完全分类,得到如下结论: 一个奇素数度1-正则Cayley图要么是双正规的双Cayley图,要么在同构意义下是已知的6类无核Cayley图的正规覆盖: 3个无限类、3个零散图,其中包括2个11度图以及1个23度图。

关键词: 1-正则, Cayley图, 无核, 正规商, 奇素数度

Abstract: A graph Γ is called 1-regular if Aut(Γ) acts regularly on its arcs. In this paper, the 1-regular Cayley graphs of valency odd prime is classified completely, and the following conclusions are obtained: a 1-regular Cayley graph of valency odd prime is either a bi-normal bi-Cayley graph or a normal covering of the known six types of core-free ones up to isomorphism, which are three infinite types, three scattered graphs, including two graphs of valency 11 and a graph of valency 23.

Key words: 1-regular, Cayley graph, core-free, normal quotient, valency odd prime

中图分类号:

O157

李靖建, 朱文英, 解雅婷. 奇素数度的1-正则Cayley图[J]. 广西师范大学学报（自然科学版）, 2019, 37(2): 121-125.

LI Jingjian, ZHU Wenying, XIE Yating. One-Regular Cayley Graphs of Valency Odd Prime[J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(2): 121-125.

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奇素数度的1-正则Cayley图

One-Regular Cayley Graphs of Valency Odd Prime

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