Algebraic Graph Theory Seminar - Yasamin Khaefi (9.10.2026)

Friday 9.10.2026 at 13:15, Lecture room M IX (online too)

07. 10. 2026 20.20 hod.
By: Martin Mačaj

Yasamin Khaefi:
Subgroup Perfect Codes and Regular Sets in Cayley Graphs

Abstract:
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.