关于交换群上的Cayley有向图的正规性

doi:10.12341/jssms10281

系统科学与数学 ›› 2005, Vol. 25 ›› Issue (6): 700-710.DOI: 10.12341/jssms10281

关于交换群上的Cayley有向图的正规性

徐明曜,张勤海,周进鑫

山西师范大学数学与计算机科学学院, 山西 041004

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2005-12-25 发布日期:2005-12-25

PDF ( 707 ) 引用被引次数 ( 12 | 1 )

徐明曜;张勤海;周进鑫. 关于交换群上的Cayley有向图的正规性[J]. 系统科学与数学, 2005, 25(6): 700-710.

Xu Mingyao;Zhang Qinhai;Zhou Jinxin. ON THE NORMALITY OF DIRECTED CAYLEY GRAPHS OF ABELIAN GROUPS[J]. Journal of Systems Science and Mathematical Sciences, 2005, 25(6): 700-710.

ON THE NORMALITY OF DIRECTED CAYLEY GRAPHS OF ABELIAN GROUPS

Xu Mingyao, Zhang Qinhai,Zhou Jinxin

School of Mathematics and Cumputer Science, Shanxi Teachers University, Shanxi 041004

Received:1900-01-01 Revised:1900-01-01 Online:2005-12-25 Published:2005-12-25

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$p^{n}(n\leq 2)$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.

关键词： Cayley有向图, 自同构群, 正规Cayley有向图

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 $p^n$ ($n\leq 2, p$ an odd prime) with valency at most 3.

Key words: Cayley graphs, automorphism groups, normal Cayley digraphs, arc-transitive graphs.

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