具有小度数的1-正则Cayley有向图

One-regular Cayley digraphs of small valency

令Γ是一个图,如果Γ的自同构群Aut(Γ)作用在其弧集上是正则的,则称图Γ为1弧正则图,简称1正则图。本文利用局部分析法和全局分析法,结合图论、群论,尤其是置换群的一些理论以及方法,给出了度数分别为3、4、5、6的1正则Cayley有向图的完全分类,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。

A graphΓis called 1-arc-regular if Aut(Γ)acts regularly on its arcs,abbreviated as 1-regular.Using local and global analysis methods,combined with graph theory,group theory,and especially some theories and methods of permutation groups,we gave a complete classification of 1-regular Cayley digraphs with degrees of 3,4,5,or 6,respectively.If such a graph is not normal or binormal,it must be a normal(multiple)covering of a quotient graph.