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点稳定子为Q8的8度1-正则Cayley图
1-regular Cayley Graph with Vertex Stabilizer Q8 of Valency 8
【摘要】 设Γ=Cay(G,S)是一个Cayley图,G≤X≤Aut(Γ).如果X作用在图Γ的1-弧上正则,则称图Γ是(X,1)-正则Cayley图.该文给出了点稳定子为8阶四元数群的8度(X,1)-正则Cayley图的一个完全分类:证明了这样的图如果不是正规或双正规的,那么它一定是某个商图的正规多重覆盖或12种无核图的正规覆盖.
【Abstract】 LetΓ=Cay(G,S)be aCayley graph,and G≤X≤Aut(Γ).A graphΓis called an(X,1)-regular Cayley graph if Xacts regularly on its 1-arcs.This paper gives acomplete classification of 8-valent(X-1)-regular Cayley graphs with Q8as its vertex stablizer,and also proves that such graphs,neither normal nor bi-normal,are normal multi-cover of quotient graphs or normal cover of 12kinds of core-free graphs.
【基金】 国家自然科学基金(10961004;11226141;11361006);广西自然科学基金(2013GXNSFAA019018;2013GXNSFBA019018;2012GXNSFBA053010);广西大学科研基金项目(XBZ110328)
- 【文献出处】 广西师范学院学报(自然科学版) ,Journal of Guangxi Teachers Education University(Natural Science Edition) , 编辑部邮箱 ,2014年01期
- 【分类号】O157.5
- 【被引频次】3
- 【下载频次】39