| D8p的连通3度Cayley有向图的正规性 |
| |
| 引用本文： | 徐尚进,张晓均,高扬.D8p的连通3度Cayley有向图的正规性[J].广西师范学院学报(自然科学版),2012,29(2):1-5. |
| |
| 作者姓名： | 徐尚进 张晓均 高扬 |
| |
| 作者单位： | 1. 广西大学数学与信息科学学院,广西南宁,530004
2. 广西大学行健文理学院,广西南宁,530005 |
| |
| 基金项目： | 国家自然科学基金项目，广西科学基金资助项目，广西研究生教育创新计划资助项目 |
| |
| 摘 要： | 称有限群G的Cayley（有向）图X是正规的,如果G的右正则表示R（G）正规于图X的全自同构群Aut（X）.该文主要研究8p阶二面体群G∶=D8p=〈a,b a4p=b2=1,b-1ab=a-1〉的连通3度Cayley有向图X∶=Cay（G,S）的正规性.并证明：（1）若p=2时,Cayley（有向）图X不正规当且仅当S~{b,a,a5}和S~{b,ba,bak}（k=3,4,5,6）.（2）若p为奇素数,Cayley（有向）图X不正规当且仅当S~{b,a,a2p＋1}和S~{b,ba,bak}（k=2p,2p＋1）.
|
| 关 键 词： | 二面体群 Cayley有向图 正规性 |
The Normality of Connected Cubic Cayley Digraphs on the Dihedral Group with Order 8p |
| |
| XU Shang-jin,ZHANG Xiao-jun,GAO Yang.The Normality of Connected Cubic Cayley Digraphs on the Dihedral Group with Order 8p[J].Journal of Guangxi Teachers Education University:Natural Science Edition,2012,29(2):1-5. |
| |
| Authors: | XU Shang-jin ZHANG Xiao-jun GAO Yang |
| |
| Institution: | 1.School of Mathematics and Information Sciences,Guangxi University,Nanning 530004,P.R.China;2.Xingjian College of Science and Liberal Art,Guangxi University,Nanning 530005,P.R.China) |
| |
| Abstract: | A Cayley(di)graph X on a finite group G is said to be normal if the acting group R(G) of the right multiplication by G is normal in its full automorphism group.In this paper,the authors mainly research the normality of connected cubic Cayley digraphs on the 8p-order dihedral group G:=D8p=〈a,ba4p=b2=1,b-1ab=a-1〉,and then prove that all such graphs X=Cay(G,S) are non-normal if and only if S~{b,a,a2p+1} and S ~{b,ba,bak }(k=2p or 2p+1) with p being an odd prime,or S~{b,a,a5} and S~{b,ba,bak}(k=3,4,5,6) with p=2. |
| |
| Keywords: | dihedral group Cayley digraph normality |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
