Seminár z algebraickej teórie grafov - Shasha Zheng (20.10.2023)

v piatok 20.10.2023 o 13:00 hod. v posluchárni M VIII aj online

17. 10. 2023 13.39 hod.
Od: Martin Mačaj

Prednášajúci: Shasha Zheng

Názov: Cayley graphs and graphical regular representations

Termín: 20.10.2023, 13:00 hod., M VIII a MS Teams

Abstrakt:
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.