一类非交换群上的正规边传递Cayley图  

A Class of Normal Edge-transitive Cayley Graphs on Non-abelian Groups

作　　者：李诺 邓奇 张华[1] LI Nuo;DENG Qi;ZHANG Hua(School of Mathematics,Yunnan Normal University,Kunming,Yunnan,650500,P.R.China;College of Arts and Sciences Kunming,Kunming,Yunnan,650221,P.R.China)

机构地区：[1]云南师范大学数学学院,云南昆明650500 [2]昆明文理学院,云南昆明650221

出　　处：《数学进展》2024年第2期257-266,共10页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.11161058,11561078)。

摘　　要：设Γ=Cay(G,S)是群G关于其子集S的Cayley图.若群G在Γ的自同构群Aut(Γ)中的正规化子作用在Γ的边集上是传递的,那么就称图Γ是正规边传递Cayley图.本文研究一类2p^(2)(p为奇素数)阶非交换群G上的正规边传递Cayley图的结构.首先列出了这类非交换群的结构及其自同构群,然后讨论了这类群上的4度正规边传递Cayley图,最后对群G上的正规边传递Cayley图进行了刻画和分类.Let G be a group and let=Cay(G,S)be a Cayley graph of G with respect to its subset S.The graphis said to be normal edge-transitive if the normalizer of G in the automorphism group Aut()ofacts transitively on the edge set of.In this paper we study normal edge-transitive Cayley graphs on a class of non-abelian groups with order 2p^(2)(p an odd prime).First we present the structural information and the automorphism groups of this class of non-abelian groups.Then we investigate the tetravalent normal edge-transitive Cayley graphs on such groups,and finally the normal edge-transitive Cayley graphs on G are characterized and classified.

关 键 词：CAYLEY图 对称图 正规边传递 

分 类 号：O157.6[理学—数学]