Normal Cayley graphs of finite groups

作     者：王长群 王殿军 徐明耀 

作者机构：1. Dapartment of System Science and Mathematics Zhengzhou University 450052 Zhengzhou China 2. Department of Applied Mathematics Tsinghua University 100084 Beijing China 3. Department of Mathematics Peking University 100871 Beijing China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：1998年第41卷第3期

页      面：242-251页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：ProjectsupportedbytheNationalNaturalScienceFoundationofChina (GrantNo .10 2 310 6 0 )andtheDoctorialProgramFoundationofInstitutionsofHigherEducationofChina 

主　　题：Cayley graph normal Cayley (di)graph. 

摘      要：LetG be a finite group and let S be a nonempty subset of G not containing the identity element 1. The Cayley (di) graph X = Cay(G, S) of G with respect to S is defined byV (X)=G, E (X)={(g,sg)|g∈G, s∈S} A Cayley (di) graph X = Cay (G,S) is said to be normal ifR(G) ?A = Aut (X). A group G is said to have a normal Cayley (di) graph if G has a subset S such that the Cayley (di) graph X = Cay (G, S) is normal. It is proved that every finite group G has a normal Cayley graph unlessG??4×?2 orG?Q 8×? 2 r (r?0) and that every finite group has a normal Cayley digraph, where Zm is the cyclic group of orderm and Q8 is the quaternion group of order 8.