【摘要】 Sn为n阶对称群,A,B是Sn的两个极小生成集,且其中的元素都为对换,Tra(A),Tra(B)则分别是A,B的对换树.Cay(Sn,A),Cay(Sn,B)分别表示群Sn关于A,B的Cayley图,证明了:Cay(Sn,A)■Cay(Sn,B)Tra(A)■Tra(B).同时也说明,同阶对称群上不同构的两Cayley图可能会有很相似的性质,如都是点传递图,自同构群相同,圈结构也相同.更多还原

【Abstract】 Let A and B be the minimal generating transposition sets of symmetric group S_n,Tra(A) Tra(B) be the Cay(S_n,A),and Cay(S_n,B) be Cayley graphs on S_n with generating set A and B respectively,in this paper,it shows that Cay(S_n,A)■Cay(S_n,B)Tra(A)■Tra(B).Following this,it is easy to see the non-isomorphism Cayley graphs which can have similar properties such as vertex-transitivity and the same automorphism groups.更多还原