论文标题
双方图形规则表示的猜想
A conjecture on bipartite graphical regular representations
论文作者
论文摘要
在本文中，我们关注的是有限群体的分类，该组承认双方drr和二分GRR。 首先，我们发现有限组的自然障碍因不承认两分GRR。然后，我们对满足这种自然障碍的有限群体进行完整的分类，因此不承认双方GRR。基于这些结果和一些广泛的计算机计算，我们指出了一个猜想，目的是对有限组进行完整的分类，该组允许双方GRR。 接下来，我们证明了大多数有限群体不承认本文中发现的二分GRR的存在。实际上，我们证明了一个更强大的结果：我们在这些组上对两分的DRR进行了渐近枚举。同样，基于这些结果和一些广泛的计算机计算，我们指出了一个猜想，目的是对有限组进行完整的分类，该群体承认双方DRR。
In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR. First, we find a natural obstruction in a finite group for not admitting a bipartite GRR. Then we give a complete classification of the finite groups satisfying this natural obstruction and hence not admitting a bipartite GRR. Based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite GRR. Next, we prove the existence of bipartite DRRs for most of the finite groups not admitting a bipartite GRR found in this paper. Actually, we prove a much stronger result: we give an asymptotic enumeration of the bipartite DRRs over these groups. Again, based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite DRR.
