论文标题
在渐近枚举卡利图上
On the asymptotic enumeration of Cayley graphs
论文作者
论文摘要
在本文中，我们对Cayley图的渐近枚举感兴趣。以前已经证明，几乎每个Cayley Digraph都具有最小的自动构型组：也就是说，这是一个挖掘规则表示（DRR）。在本文中，我们解决了无向Cayley图的相应问题。由于有两个无限的群体家庭不承认任何图形规则代表（GRR），因此情况变得复杂。 Digraphs的策略涉及分别分析常规组$ r $具有非平凡的正常亚组$ n $的情况，该属性与Digraph的自动形态组修复了每个$ n $ coset setwise的属性，以及没有的情况。在本文中，我们处理了普通组具有这种非平凡的正常亚组的情况下的无方向图。
In this paper we are interested in the asymptotic enumeration of Cayley graphs. It has previously been shown that almost every Cayley digraph has the smallest possible automorphism group: that is, it is a digraphical regular representation (DRR). In this paper, we approach the corresponding question for undirected Cayley graphs. The situation is complicated by the fact that there are two infinite families of groups that do not admit any graphical regular representation (GRR). The strategy for digraphs involved analysing separately the cases where the regular group $R$ has a nontrivial proper normal subgroup $N$ with the property that the automorphism group of the digraph fixes each $N$-coset setwise, and the cases where it does not. In this paper, we deal with undirected graphs in the case where the regular group has such a nontrivial proper normal subgroup.
