The Classification of Connected Imprimitive Arc-transitive Graphs on Zp×Zp

被引：0

作者：

李学文

徐明曜

机构：

[1] School of Mathematical Sciences Peking University,Beijing,100871 P.R.China

[2] Mathematics Department,Tangshan Teachers’College,Tangshan,Hebei,063000,P.R.China,School of Mathematical Sciences Peking University,Beijing,100871 P.R.China

来源：

数学进展 | 2005年 / 03期

基金：

美国国家科学基金会;

关键词：

The Classification of Connected Imprimitive Arc-transitive Graphs on Zp; Zp;

D O I：

暂无

中图分类号：

O157.5 [图论];

学科分类号：

070104 ;

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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页码：373 / 374

页数：2