Fakulta matematiky, fyziky
a informatiky
Univerzita Komenského v Bratislave

Algebraic Graph Theory Seminar - Shasha Zheng (20.10.2023)

Friday 20.10.2022 at 13:00, Lecture room M/VIII (online too)


17. 10. 2023 13.45 hod.
Od: Martin Mačaj

Shasha Zheng:
Cayley graphs and graphical regular representations


Abstract:
In this talk we are concerned with the symmetry of Cayley graphs. Here are some natural questions: What kind of automorphism group of a Cayley graph is 'typical'; what kind of Cayley graph is '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 with the lowest level of symmetry would be the most common ones. We estimate the number of graphical regular representations of a given group with large enough order and, based on some previously known results, show that almost all finite Cayley graphs have full automorphism groups 'as small as possible’.

Involving joint work with Binzhou Xia.

Those of you who are not able to attend in person or who are still uncertain about the safety of attending in person are welcome to attend via MS Teams. In either case, we hope to see as many of you as possible (either in person or virtually) at our Friday gatherings.