| The Classification of Connected Imprimitive Arc-transitive Graphs on Zp × Zp |
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| 引用本文： | 李学文,徐明曜.The Classification of Connected Imprimitive Arc-transitive Graphs on Zp × Zp[J].数学进展,2005,34(3):373-374. |
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| 作者姓名： | 李学文 徐明曜 |
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| 作者单位： | School of Mathematical Sciences Peking University，Beijing，100871 P.R.China，Mathematics Department，Tangshan Teachers’College，Tangshan，Hebei，063000，P.R.China，School of Mathematical Sciences Peking University，Beijing，100871 P.R.China |
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| 基金项目： | Project supported by the National Science Foundation of China under grant(No．103710003)． |
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| 摘 要： | The term (di)graph is employed to mean that a graph in question is either a directed graph or an undirected graph.The symbol G(p,r)represents the digraph defined by Chao: V(G(p,r))=Zp,E(G(p,r))={(x,y)|x-y∈Hr},where P is a prime,r is a positive divisor of P-1 and Hr is the unique subgroup of order r in Aut(Zp).A Cayley graph (?)=Cay(G,S)is called imprimitive if A=Aut((?))acts imprimitively on V((?)).Let (?)=Cay(G,S)be a connected imprimitive arc-transitive graph on G=Z×Z,B={B0,B1,…,Bp-1}the complete block system of A=Aut((?))on V((?))=G and K the kernel of A on B.Then obviously K≠1.
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| 修稿时间： | 2005年4月1日 |
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