关于交换群上的Cayley有向图的正规性

ON THE NORMALITY OF DIRECTED CAYLEY GRAPHS OF ABELIAN GROUPS

Cayley有向图X=Cay(G,S)叫做正规的,如果G的右正则表示R(G)在X的全自同构群Aut(X)中正规,我们定出了交换群上的小度数的非正规的Cayley有向图, 并给出了一个猜想．应用这个结果,给出了pn(n≤2)个点上的度数不超过3的有向对称图的分类,这里p是一个奇素数．

A direced Cayley graph X = Cay（G, S） is called normal for G if the right representation R（G） of G is normal in the full automorphism group Aut（X）. In this paper, we determine all non-normal directed Cayley graphs of finite abelian groups with valencies 2 and 3. Using the result, we give a complete classification of connected directed arc-transitive graphs of order p^n（n≤2,p an odd prime） with valency at most 3.