| 关于交换群上的Cayley有向图的正规性 |
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| 引用本文： | 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 |
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| 作者姓名： | 徐明曜 张勤海 周进鑫 |
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| 作者单位： | 山西师范大学数学与计算机科学学院,山西,041004 |
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| 基金项目： | 国家自然科学基金(10371003,10471085)山西省自然科学基金(20051007)教育部重点项目基金(02023)山西省留学回国人员基金([2004]7)资助课题． |
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| 摘 要： | 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．
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| 关 键 词： | Cayley有向图 自同构群 正规Cayley有向图 对称图 |
| 修稿时间： | 2003-09-15 |
ON THE NORMALITY OF DIRECTED CAYLEY GRAPHS OF ABELIAN GROUPS |
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| 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 |
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| Authors: | Xu Mingyao Zhang Qinhai Zhou Jinxin |
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| Affiliation: | School of Mathematics and Cumputer Science, Shanxi Teachers University, Shanxi 041004 |
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| Abstract: | A direced Cayley graph $X=cay(G, S)$ is called normal for $G$ ifthe right representation $R(G)$ of $G$ is normal in the fullautomorphism group $Aut (X)$. In this paper, we determine allnon-normal directed Cayley graphs of finite abelian groups withvalencies 2 and 3. Using the result, we give a complete classificationof connected directed arc-transitive graphs of order $p^n$ ($nleq 2, p$ an odd prime) with valency at most 3. |
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| Keywords: | Cayley graphs automorphism groups normal Cayley digraphs arc-transitive graphs. |
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