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Recent Advances in Graphical Regular Representations of Groups

夏彬绉 Binzhou Xia

The University of Melbourne

Time: 16:30-17:30 (GMT+8), Tuesday September 26th, 2023
Location: Zoom

Abstract: The question of whether a group can be represented as the automorphism group of a graph was addressed in the early stages of graph theory. If a group \(G\) is isomorphic to the automorphism group of a Cayley graph \(\Gamma\) of \(G\), then \(\Gamma\) is said to be a Graphical Regular Representation (GRR) of \(G\). A classic result, established in the 1970s through a series of papers by various authors, determines which groups possess GRRs. In this talk, I will delve into the more recent developments in GRRs, encompassing asymptotic enumeration, GRRs with prescribed valency, and some variations of GRRs.

Host: 黄弘毅 Hong Yi Huang