二面体群的小度数Cayley图的同构类的计数

Enumeration of Isomorphism Types of Cayley Graphs of Small Valencies on Dihedral Groups

中文关键词:  二面体群  Cayley图  图的同构.

英文关键词:dihedral group  Cayley graph  isomorphisms of graphs.

中文摘要:

      设G是有限群，S是G的一个不包含单位元的非空子集且满足S^-1=S，定义群G关于S一个的Cayley图x=Cay(G，S)如下：V(X)=G，E(X)=｛(g，sg)｜g∈G,s∈S}.对于素数P，本文给出了2p阶的二面体群的3度和4度Cayley图的同构类的个数.

英文摘要:

      Let G be a finite group and a subset of G not containing the identity element of G. A Cayley graph X = Cay (g,S) of G with S is defined by V (X) = G, E (X) = ( (g, sg) ｜ g ∈ G, s ∈ S }. In this paper, we calculate the number of isomorphism types of all Cayley graphs of valencies 3 and 4 of dihedral groups of order twice a prime.