论文标题
图形规则表示的渐近枚举
Asymptotic enumeration of graphical regular representations
论文作者
论文摘要
我们估计给定组的图形规则表示（GRR）的数量，该数字具有足够大的阶段。结果，我们表明，几乎所有有限的开饼图都“尽可能小”具有完整的自动形态群体。这证实了Babai-Godsil-Imrich-Lovasz在GRR的比例中的猜想，以及在给定有限群的Cayley图中的XU的猜想。
We estimate the number of graphical regular representations (GRRs) of a given group with large enough order. As a consequence, we show that almost all finite Cayley graphs have full automorphism groups 'as small as possible'. This confirms a conjecture of Babai-Godsil-Imrich-Lovasz on the proportion of GRRs, as well as a conjecture of Xu on the proportion of normal Cayley graphs, among Cayley graphs of a given finite group.
