图正则表示的渐近枚举

IF 1.5 1区数学 Q1 MATHEMATICS

Proceedings of the London Mathematical Society Pub Date : 2023-09-25 DOI:10.1112/plms.12563

Binzhou Xia, Shasha Zheng

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引用次数: 1

摘要

摘要我们估计了给定组中具有足够大阶数的图形正则表示(grr)的个数。因此，我们证明了几乎所有有限Cayley图都具有“尽可能小”的完全自同构群。这证实了Babai-Godsil-Imrich-Lovász关于grr的比例的一个猜想，以及Xu关于给定有限群的Cayley图中正规Cayley图比例的一个猜想。

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Asymptotic enumeration of graphical regular representations

Abstract 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–Lovász 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.

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来源期刊

Proceedings of the London Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Proceedings of the London Mathematical Society is the flagship journal of the LMS. It publishes articles of the highest quality and significance across a broad range of mathematics. There are no page length restrictions for submitted papers. The Proceedings has its own Editorial Board separate from that of the Journal, Bulletin and Transactions of the LMS.