4p阶二面体群连通3度Cayley有向图的正规性

设G是一个有限群,S是G的不包含单位元1的非空子集,定义群G关于S的Cayley(有向)图X:=Cay(G,S)如下:V(X)=G,E(X)={(g,sg)|g∈G,s∈S}.Cayley(有向)图X:=Cay(G,S)称为正规的,如果G的右正则表示R(G)在X的自同构群Aut(X)中是正规的.设G是4p阶二面体群(p为素数).考察了Cay(G,S)连通3度的正规性,并给出了这些图的全自同构群.

On the Normality of Cayley Digraph of Dihedral Group of Order 4p on 3 Degrees Connectivity

Let G be a finite group and S a subset of G not containing the identity element 1.The Cayley digraph X=Cay(G,S) of G on S is defined by V(X)=G,E(X)={(g,sg)|g∈G,s∈S}.A Cayley(di)graph X=Cay(G,S) is called normal if right regular representation of G is a normal subgroup of automorphism group of X.Let G is a dihedral group(p for prime numbers).In This paper we research the normality of Cayley Digraph on 3 degrees of connectivity,and these graph are given the full automorphism group.