| On the Classification of Arc-transitive Circulant Digraphs of Order Odd-Prime-Squared |
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| 作者姓名： | Xue Wen LI |
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| 作者单位： | [1]LMAM ＆ School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China [2]Department of Mathematics, Tangshan Teacher＇s College, Tangshan 063000, P. R. China |
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| 基金项目： | Research supported by the National Natural Science Foundation of China under Grant No. 103710003 |
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| 摘 要： | A Cayley graph F = Cay（G, S） of a group G with respect to S is called a circulant digraph of order pk if G is a cyclic group of the same order. Investigated in this paper are the normality conditions for arc-transitive circulant （di）graphs of order p^2 and the classification of all such graphs. It is proved that any connected arc-transitive circulant digraph of order p^2 is, up to a graph isomorphism, either Kp2, G（p^2,r）, or G（p,r）pK1], where r｜p- 1.
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| 关 键 词： | Cayley图表 循环行列式 初始序列 同类图 |
| 收稿时间： | 2003-06-10 |
| 修稿时间： | 2003-06-102004-04-26 |
On the Classification of Arc-transitive Circulant Digraphs of Order Odd–Prime–Squared |
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| Xue Wen LI.On the Classification of Arc-transitive Circulant Digraphs of Order Odd-Prime-Squared[J].Acta Mathematica Sinica,2005,21(5):1131-1136. |
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| Authors: | Xue Wen Li |
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| Institution: | (1) LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China;(2) Department of Mathematics, Tangshan Teacher’s College, Tangshan 063000, P. R. China |
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| Abstract: | A Cayley graph Γ = Cay(G, S) of a group G with respect to S is called a circulant digraph
of order p
k
if G is a cyclic group of the same order. Investigated in this paper are the normality
conditions for arc–transitive circulant (di)graphs of order p
2 and the classification of all such graphs. It
is proved that any connected arc–transitive circulant digraph of order p
2 is, up to a graph isomorphism,
either
, G(p
2, r), or G(p, r)pK
1], where r | p − 1.
Research supported by the National Natural Science Foundation of China under Grant No. 103710003 |
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| Keywords: | Cayley graph Normal Cayley graph Circulant digraph |
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