Seminár z algebraickej teórie grafov - Yasamin Khaefi (9.10.2026)

v piatok 9.10.2026 o 13:15 hod. v miestnosti M IX (aj online)

07. 10. 2026 20.11 hod.
Od: Martin Mačaj

Prednášajúci: Yasamin Khaefi

Názov prednášky: Subgroup Perfect Codes and Regular Sets in Cayley Graphs

Termín: 9.10.2026, 13:15 hod., M IX, MS Teams

Abstrakt:
Perfect codes (also known as efficient dominating sets) in Cayley graphs provide a natural connection between coding theory, graph theory, and group theory. In this talk, I will focus on perfect codes that are subgroups of the underlying group. After introducing the basic concepts and some known characterizations, I will discuss how the existence of subgroup perfect codes is related to Sylow 2-subgroups and present some further results on this topic.

I will then consider the connection between perfect codes and regular sets in Cayley graphs. In particular, I will discuss conditions under which a subgroup is a perfect code if and only if it is an (a,b)-regular set.