Journal of Guangxi Normal University(Natural Science Edition) ›› 2013, Vol. 31 ›› Issue (2): 51-54.

Previous Articles     Next Articles

1-Regular Hexavalent Cayley Graphs with Abelian Point Stabilizer

LI Jing-jian1,2, XU Shang-jin2, WANG Rui2   

  1. 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

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

CLC Number: 

  • O157
[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.
[1] 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.
[2] HUA Xiao-hui, CHEN Li. Isomorphisms and Automorphisms of Coset Graphs [J]. Journal of Guangxi Normal University(Natural Science Edition), 2015, 33(4): 68-72.
[3] 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.
[4] 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.
[5] XU Shang-jin, ZHANG Xiao-jun, KANG Zhe, LI Jing-jian. Tetravalent Connected Half-transitive Graphs of Order qp2 [J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(2): 54-58.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright © Journal of Guangxi Normal University(Natural Science Edition), All Rights Reserved.
Tel: 0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
Powered by Beijing Magtech Co. Ltd