若干类满足■dm猜想的循环图

Some Classes of Satisfying ■dm Conjecture's Circulant

本文对阶数为素数幂n=p^n的循环图,讨论了它关于Adam同构的问题。对于无向循环图G_n(K),其中K={a_i,n-a_i|0<a_i<n-a_i,i=1,2,…,k}且k≤p,证明了G_n(K)满足Adam猜想。本文还构造了一类同构但不满足Adam猜想的循环图,从而说明对于素数幂这里得到的结果是最好的。此外,还得到了另外几类满足Adam猜想的循环图,并且讨论了循环图的补图的Adam同构性质。

In this paper, we discussed the problom of ■dm isomorphism for prime power n=p^a, and obtained the result that for circulant digraph G_n(K), K={a_o|0<a_1<n, i=1,2,…,k}, k≤p, and circulant G_n(K) K{a_i, n-a_i|0<a_i<n-a_i, i=1, 2,…,k}. k≤p, They both satisfy Adám conjecture. Moreover, we constructed a classes of ciculants which do not agree with Adam conjecture. In this way, the result obtained here is shown to be better. Additionally, we also discussed the problem of Adam isomorphism of complement of circulant.