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Graphical regular representations of finite groups

郑莎莎 Shasha Zheng

University of Melbourne (墨尔本大学)

Time: 16:00-18:00 (GMT+8), Monday April 3rd, 2023
Location: Zoom

Abstract: In this talk we are concerned with the automorphisms of Cayley graphs. Here are some natural questions: What kind of automorphism groups of Cayley graphs are ‘typical’; what kind of Cayley graphs are ‘common’? Viewing that ‘symmetry is rare’, a rough guess for the first question would be the groups that are ‘as small as possible’ in some sense, and one may guess for the second question that the Cayley graphs having the ‘smallest’ full automorphism groups would be the most common ones. We will estimate the number of GRRs of a given group with large enough order and show that almost all finite Cayley graphs have full automorphism groups ‘as small as possible’.

Host: 丁兆宸 Zhaochen Ding