【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K_2,2,2的弧传递Z_n-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.更多还原

【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 Z_n-regular coverings of K_2,2,2,and obtain several new infinite families of 4-valent symmetric graphs as the covering graphs of K_2,2,2 by Z_n,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.更多还原