p^2阶弧传递循环图的正规性条件

The Condition for the Normality of Arc-transitive Circulant Graphs of order Prime-squared

群G关于S的有向Cayley图X=Cay(G,S)称为pk阶有向循环图,若G是pk阶循环群.利用有限群论和图论的较深刻的结果,对p2阶弧传递(有向)循环图的正规性条件进行了讨论,证明了任一p2阶弧传递(有向)循环图是正规的当且仅当(|Aut(G,S)|,p)=1.

A Cayley graph X = Cay（G, S） of group G with respect to S is called a circulant digraph of order p^k if G is a clrculant group of order p^k Disscussed in this paper is the condition for a circulant （di）graph of order p^2 to be normal. We prove that a circulant （di）graph of order p^2 is normal if and only if （｜Aut（G,S）｜, p） = 1.