节点文献
完全三部图K2,2,2的弧传递Zn-正则覆盖
On Arc-transitive Zn-regular Coverings of K2,2,2
【作者】 王新中;
【导师】 王长群;
【作者基本信息】 郑州大学 , 基础数学, 2009, 硕士
【摘要】 设Г是有限无向简单正则图.若Г没有孤立点,我们称图Г是弧传递的或对称的,如果Г的自同构群Aut(Г)传递地作用在Г的弧集合上.本文讨论了完全三部图K2,2,2的弧传递Zn-正则覆盖,得到了几类新的4度对称图,其中n=4k或n=4k且k≡2(mod 4).特别地,我们得到了一类新的点稳定子无界并且不是两图的字典式积的4度对称图.
【Abstract】 LetГbe a finite undirected simple regular graph which has no isolated vertices.We say thatГis arc-transitive or symmetric graph,if its full automorphism group Aut(Г) acts transitively on its arc set.In this paper,we investigate the arc-transitive Zn-regular coverings of K2,2,2,and obtain several new infinite families of 4-valent symmetric graphs as the covering graphs of K2,2,2 by Zn,where n=4k or n=4k and k=2(mod 4).In particular,we obtain an infinite family of 4-valent symmetric graphs,which are not a lexicographic product of two graphs and has unboundary order of the vertex-stabilizer.
【Key words】 K2,2,2; symmetric graph; regular covering; cycle covering; voltage; lifting;
- 【网络出版投稿人】 郑州大学 【网络出版年期】2011年 S1期
- 【分类号】O157.5
- 【下载频次】10