You are here: Seminars > 2025 > October 22nd
The University of Melbourne
Time: 16:00-17:00 (GMT+8), Wednesday 22nd, 2025
Location: Zoom
Abstract:
A perfect code in a graph \(\Gamma=(V,E)\) is a subset \(C\) of \(V\) such that no two vertices in
\(C\) are adjacent and every vertex in \(V{\setminus}C\) is adjacent to exactly one vertex in \(C\).
A subgroup \(H\) of a group \(G\) is called a subgroup perfect code of \(G\) if it is a perfect code in some Cayley graph of \(G\).
In this talk, we initiate a study of which maximal subgroups of a group can occur as perfect codes.
We develop a general framework for this problem and propose several related questions.
Host: 甘芸松 Yunsong Gan