共查询到15条相似文献,搜索用时 860 毫秒
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设G是一个有限群,S是G的不包含单位元1的非空子集,定义群G关于S的Cayley(有向)图X:=Cay(G,S)如下:V(X)=G,E(X)={(g,sg)|g∈G,s∈S}.Cayley(有向)图X:=Cay(G,S)称为正规的,如果G的右正则表示R(G)在X的自同构群Aut(X)中是正规的.设G是4p阶二面体群(p为素数).考察了Cay(G,S)连通3度的正规性,并给出了这些图的全自同构群. 相似文献
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群G的Cayley有向图X=Cay(G,S)叫做正规的,如果G的右正则表示R(G)在X的全自同构群Aut(X)中正规.决定了6p(p素数)阶2度有向Cayley图的正规性,发现了一个新的2度非正规Cayley有向图. 相似文献
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《数学的实践与认识》2013,(23)
有限群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在AutX中正规.研究了一类16p阶群G=〈a,b|a(8p)=b(8p)=b2=1,a2=1,ab=ab=a(4p-1)〉的3度无向连通Cayley图的正规性,其中p为奇素数,并得到该群的正规与非正规的Cayley图 相似文献
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李学文 《数学的实践与认识》2005,35(8):233-238
群G关于S的有向Cayley图X=Cay(G,S)称为pk阶有向循环图,若G是pk阶循环群.利用有限群论和图论的较深刻的结果,对p2阶弧传递(有向)循环图的正规性条件进行了讨论,证明了任一p2阶弧传递(有向)循环图是正规的当且仅当(|Aut(G,S)|,p)=1. 相似文献
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二面体群D_(2n)的4度正规Cayley图 总被引:4,自引:0,他引:4
设G是有限群,S是G的不包含单位元1的非空子集.定义群G关于S的 Cayley(有向)图X=Cay(G,S)如下:V(x)=G,E(X)={(g,sg)|g∈G,s∈S}. Cayley图X=Cay(G,S)称为正规的如果R(G)在它的全自同构群中正规.图X称为1-正则的如果它的全自同构群在它的弧集上正则作用.本文对二面体群D2n以Z22 为点稳定子的4度正规Cayley图进行了分类. 相似文献
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半二面体群的小度数Cayley图 总被引:1,自引:0,他引:1
群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在Aut X中正规.研究了4m阶半二面体群G=〈a,b a2m=b2=1,ab=am-1〉的3度和4度Cayley图的正规性,其中m=2r且r>2,并得到了几类非正规的Cayley图. 相似文献
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群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在AutX中正规.研究了4m阶拟二面体群G=a,b|a~(2m)=b~2=1,a~b=a~(m+1)的4度Cayley图的正规性,其中m=2~r,且r2,并得到拟二面体群的Cayley图的同构类型. 相似文献
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主要给出几类非交换群对Alspach猜想(当Cay(G,S)的度小于等于4时)成立,进一步对2n和2p2阶群Cayley图的Hamilton圈的分解进行了讨论. 相似文献
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GUO Dachang 《系统科学与数学》2000,13(1)
Let G be a finite group and S a subset of G not containing the identity element 1. We define the Cayley (di)graph X = Cay(G, S) of G with respect to S by V(X) = G,E(X) = {(g, sg) [ g ∈ G, s ∈ S}. A Cayley (di)graph X = Cay(G, S) is called normal if GR A = Aut(X). In this paper we prove that if S = {a, b, c} is a 3-generating subset of G = A5 not containing the identity 1, then X = Cay(G, S) is a normal Cayley digraph. 相似文献
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Jin-xin ZHOU & Yan-quan FENG Department of Mathematics Beijing Jiaotong University Beijing China 《中国科学A辑(英文版)》2007,50(2):201-216
A Cayley graph Cay(G, S) on a group G is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of Cay(G, S). In this paper, two sufficient conditions for non-normal Cayley graphs are given and by using the conditions, five infinite families of connected non-normal Cayley graphs are constructed. As an application, all connected non-normal Cayley graphs of valency 5 on A5 are determined, which generalizes a result about the normality of Cayley graphs of valency 3 or 4 on A5 determined by Xu and Xu. Further, we classify all non-CI Cayley graphs of valency 5 on A5, while Xu et al. have proved that As is a 4-CI group. 相似文献
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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≅ℤ4×ℤ2 orG≅Q
8×ℤ
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.
Project supported by the National Natural Science Foundation of China (Grant No. 10231060) and the Doctorial Program Foundation of Institutions of Higher Education of China. 相似文献
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