摘要
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)在图X的全自同构群Aut(X)中正规.决定Cayley图Cay(G,S)是否正规,对于确定它的自同构群的结构有重要意义.设p,q为奇素数,q<p且q|(p-2).本文综合运用有限群的知识与图的组合技巧,证明了两类2pq阶群G=〈a,b|apq=b2=1,ab=ar〉,r=±(p-1)的所有3度无向连通Cayley图都是正规的,并完成了对它们的分类.作为这一结果的应用,决定了这两类群的弱3-CI性质,并给出了一个不同构的群可以具有同构的Cayley图的例子.
For a finite group G,a Cayley graph Cay(G,S) is said to be normal ,if the group R(G) of right translations on G is a normal subgroup of the full automorphism group of Cay(G,S). Let G= (a,b[ a^pq =b^2 = 1 ,a^b =a^r) ,where p,q are odd primes,q〈p,q [ (p- 2), r= ± (p- 1). Assume that S be a generating set of G, | S | : 3. In this paper, we classify all of the connected 3-valent Cayley graphs of G,and show that any connected 3-valent Cayley graph X:Cay(G,S) of G is normal. As applications,the weak 3-CI property of G and an example of that non-isomorphic groups can have the isomorphic Cayley graphs were given.
出处
《厦门大学学报(自然科学版)》
CAS
CSCD
北大核心
2009年第1期6-10,共5页
Journal of Xiamen University:Natural Science
基金
国家自然科学基金(10571013)资助