Journal of Guangxi Normal University(Natural Science Edition) ›› 2014, Vol. 32 ›› Issue (4): 66-71.

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

XU Shang-Jin1,2, QIN Yan-li1,2, ZHANG Yue-feng1,2, LI Jing-jian1,2   

  1. 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

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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

CLC Number: 

  • O157
[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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