具有交换点稳定子群的6度1-正则Cayley图

广西师范大学学报（自然科学版） ›› 2013, Vol. 31 ›› Issue (2): 51-54.

具有交换点稳定子群的6度1-正则Cayley图

李靖建^1,2, 徐尚进², 王蕊²

1.云南大学数学与统计学院,云南昆明650031;
2.广西大学数学与信息科学学院,广西南宁530004

收稿日期:2013-01-20 出版日期:2013-06-20 发布日期:2018-11-26
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(11226141);广西自然科学基金资助项目(2012GXNSFBA053010,2013GXNSF-AA019018,2013GXNSFBA019018);广西大学科研基金资助项目(XBZ110328)

1-Regular Hexavalent Cayley Graphs with Abelian Point Stabilizer

LI Jing-jian^1,2, XU Shang-jin², WANG Rui²

1.School of Mathematics and Statistics,Yunnan University,Kunming Yunnan 650031,China;
2.School of Mathematics and Information Sciences,Guangxi University,Nanning Guangxi 530004,China

Received:2013-01-20 Online:2013-06-20 Published:2018-11-26

摘要/Abstract

摘要： 令Γ是一个图,如果Γ的图自同构群Aut(Γ)作用在其弧集上正则,则称图Γ为1-正则图。本文给出具有交换点稳定子群的6度1-正则Cayley图的一个完全分类,证明了在同构意义下具有交换点稳定子群的无核6度1-正则Cayley图只有一个。

关键词: 1-正则, Cayley图, 无核, 小度数

Abstract: A graph Γ is called 1-regular if Aut(Γ) acts regularly on its arcs.In this paper,a complete characterization for 1-regular 6-valent Cayley graphs with an abelian point stabilizer is presented.It is proved that there exists only one core-free 1-regular 6-valent Cayley graph with an abelian point stabilizer.

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

中图分类号:

O157

李靖建, 徐尚进, 王蕊. 具有交换点稳定子群的6度1-正则Cayley图[J]. 广西师范大学学报（自然科学版）, 2013, 31(2): 51-54.

LI Jing-jian, XU Shang-jin, WANG Rui. 1-Regular Hexavalent Cayley Graphs with Abelian Point Stabilizer[J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(2): 51-54.

参考文献

[1] LI Cai-heng.Finite s-arc transitive Cayley graphs and flag-transitive projective planes[J].Proc Amer Math Soc,2005,133(1):31-41.
[2] 徐尚进,孙莉敏,刘翠明,等.三类2q²p阶群的3度Cayley图[J].广西师范大学学报:自然科学版,2010,28(2):30-33.
[3] WANG Chang-qun,XIONG Sheng-li.An finite family of one-regularand 4-valent Cayley graphs of quasi-dihedral groups[J].Journal of Zhengzhou University:Nataural Science Edition,2004,36(1):7-11.
[4] CONDER M D E,PRAEGER C E.Remarks on path-transitivity in finitegraphs[J].European Journal of Combinatorics,1996,17(4):371-378.
[5] FRUCHT R.A one-regular graph of degree three[J].Can J Math,1952,4(3):240-247.
[6] LI Jing-jian,LU Zai-ping.Cubic s-transitive Cayley graphs[J].Discrete Math,2009,309(3):6014-6025.
[7] XU Shang-jin,FANG Xin-gui.5-arc transitive cubic Cayley graphson finite simple groups[J].European J Combin,2007,28(3):1023-1036.
[8] CONWAY J H,CURTIS R T,NORTON S P,et al.Atlas of finite groups[M].Oxford:Clarendon Press,1985.
[9] DIXON J D,MORTIMER B.Permutation groups[M].New York:Springer-verlag,1996.
[10] HUPPERT B,BLACKBURN N.Finite groups Ⅲ[M].Berlin:Springer-verlag,1982.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed