广义四元数群的小度数Cayley图  

On Cayley Graphs of Small Valencies of Generalized Quaternion Groups

作　　者：徐尚进[1] 邓芸萍[1] 覃建军[1] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《广西民族大学学报（自然科学版）》2008年第1期45-49,共5页Journal of Guangxi Minzu University ：Natural Science Edition

基　　金：国家自然科学基金项目(10161001);广西自然科学基金项目(0542044);广西研究生教育创新计划资助项目(2007105930701M33)

摘　　要：完整解决了广义四元数群Q4pm(p为奇素数,m为正整数)的连通4度及5度无向Cayley图的CI性、正规性和弧传递性.(1)关于CI性,证明广义四元数群Q4pm都是弱5-CI的;(2)关于正规性和弧传递性,证明广义四元数群Q4pm的连通4度Cayley图在同构意义下只有两类图,其中一类正规不弧传递,另一类不正规但弧传递;而广义四元数群Q4pm的连通5度Cayley图在同构意义下也只有两类图,其中一类正规,另一类不正规,而且两类图都非弧传递.This paper perfectly resolves the CI property, normality and arc-transitive property of connected Cayley graphs of valencies 4 and 5 on generalized quaternion groups Q4p^m（p is odd prime, m is positive integer）. （1） About CI property, we prove that generalized quaternion groups Q4p^m are weak 5-CI groups; （2） About normality and arc-transitive property, we prove that the connected Cayley graphs of valency 4 on generalized quaternion groups Q4p^m have only two classes on the base of isomorphism, one is normal and non -arc-transitive, the other is non-normal bur arc-transitive; and the connected Cayley graphs of valency 5 on generalized quaternion groups Q4p^m have only two classes on the base of isomorphism too, one is normal, the other is non-normal, and these two classes of graphs are non- arc- transitive.

关 键 词：广义四元数群 自同构群 正规CAYLEY图 弱CI性. 

分 类 号：O157[理学—数学]