6度1-正则Cayley图1-regular Cayley graphs of valency 6
李靖建;徐尚进;杨旭;
摘要(Abstract):
试图对6度1-正则Cayley图给一个完全分类.利用无核的概念将图自同构群归结到对称群S6的子群.然后根据1-正则图的性质构造出所有可能的具有非交换点稳定子群的无核6度1-正则Cayley图,进一步证明了构造出的图都是有核的,由此给出了这一类图的一个完全分类.
关键词(KeyWords): 1-正则;Cayley图;无核
基金项目(Foundation): 国家自然科学基金(10961004,11226141,11361006);; 广西自然科学基金(2013GXNSFAA019018,2013GXNSFBA019018)
作者(Authors): 李靖建;徐尚进;杨旭;
参考文献(References):
- [1]Li C H.Finite s-arc transitive Cayley graphs and flag-transitive projective planes[J].Proc.Amer.Math.Soc.,2005,133(2):31-40.
- [2]Frucht R.A one-regular graph of degree three[J].Can.J.Math.,1952,4(1):240-247.
- [3]Conder M D E,Praeger C E.Remarks on path-transitivity in finite graphs[J].European J.Combin.,1996,17(4):371-378.
- [4]Li Jingjian,Lu Zaiping.Cubic s-transitive Cayley graphs[J].Discrete Math.,2009,309(3):6014-6025.
- [5]Xu Shangjin,Fang Xingui.5-arc transitive cubic Cayley graphs on finite simple groups[J].European J.Combin.,2007,28(4):1023-1036.
- [6]Conway J H,Curtis R T,Norton S P,et al.Atlas of Finite Groups[M].Oxford:Oxford University Press,1985.
- [7]Huppert B,Blackburn N.Finite Groups III[M].New York:Springer-Verlag,1982.