具有初等交换点稳定子的9度1-正则Cayley图

广西师范大学学报（自然科学版） ›› 2014, Vol. 32 ›› Issue (4): 66-71.

具有初等交换点稳定子的9度1-正则Cayley图

徐尚进^1,2, 秦艳丽^1,2, 张跃峰^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 发布日期:2018-09-26
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(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)

1-Regular Cayley Graphs of Valency 9 with Elementary Abelian Vertex Stabilizer

XU Shang-Jin^1,2, QIN Yan-li^1,2, ZHANG Yue-feng^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 Published:2018-09-26

摘要/Abstract

摘要： 对于一个图Γ,如果它的图自同构群Aut(Γ)作用在它的弧集上正则,则称图Γ为1-正则图。本文给出了具有初等交换点稳定子的9度1-正则Cayley图的一个完全分类,证明了在同构意义下,具有初等交换点稳定子的9度无核1-正则Cayley 图只有一个。

关键词: 1-正则, Cayley 图, 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 classifcation for 1-regular Cayley graphs of valency 9 with the vertex stabilizer being elementary abelian is presented. It is proved that there exists only one core-free 1-regular Cayley graphs of valency 9 with an elementary abelian vertex stabilizer.

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

中图分类号:

O157

徐尚进, 秦艳丽, 张跃峰, 李靖建. 具有初等交换点稳定子的9度1-正则Cayley图[J]. 广西师范大学学报（自然科学版）, 2014, 32(4): 66-71.

XU Shang-Jin, QIN Yan-li, ZHANG Yue-feng, LI Jing-jian. 1-Regular Cayley Graphs of Valency 9 with Elementary Abelian Vertex Stabilizer[J]. Journal of Guangxi Normal University(Natural Science Edition), 2014, 32(4): 66-71.

参考文献

[1] FRUCHT R. A one-regular graph of degree three[J]. Canad J Math,1952,4: 240-247.
[2] MARUSIC D. A family of one-regular graphs of valency 4[J]. Europ J Combinatorics,1997,18(1): 59-64.
[3] MALNIC A,MARUSIC D, SEIFTER N. Constructing infinite one-regular graphs[J]. Europ J Combinatorics,1999,20(8): 845-853.
[4] CONDER M D E, PRAEGER C E. Remarks on path-transitivity infinite graphs[J]. Europ J Combinatorics, 1996, 17(4): 371-378.
[5] LI Cai-heng. Finite s-arc transitive Cayley graphs and flag-transitive projective planes[J]. Proc Amer Math Soc, 2005,133(1): 31-41.
[6] LI Jing-jian, LU Zai-ping. Cubic s-arc transitive Cayley graphs[J]. Discrete Math,2009,309(20): 6014-6025.
[7] 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.
[8] WANG Chang-qun, XIONG Sheng-li. An finite family of one-regular and 4-valent Cayley graphs of quasi-dihedral groups[J]. Journal of Zhengzhou University: Natural Science Edition, 2004, 36(1):7-11.
[9] FANG Xin-gui, PRAEGER C E. Finite two-arc transitive graphs admitting a Suzuki simple group[J]. Comm Algebra,1999,27(8): 3727-3754.
[10] LI Cai-heng, LU Zai-ping, ZHANG Hua. Tetravalent edge-transitive Cayley graphs with odd number of vertices[J]. Journal of Combinatorial Theory: Series B, 2006,96(1): 164-181.
[11] ALAEIYAN M. Arc-transitive and s-regular Cayley graphs of valency 5 on Abelian groups[J]. Discus siones Mathematicae Graph Theory,2006,26(3): 359-368.
[12] XU Shang-jin, FANG Xin-gui, WANG Jie, et al. 5-arc transitive cubic Cayley graphs on finite simple groups[J]. European J Combinatorics, 2007,28(3): 1023-1036.
[13] DIXON J D, MORTIMER B. Permutation Groups[M]. Berlin: Springer-Verlag,1996.

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