Title: Perfect codes in Cayley graphs
Speaker: Sanming Zhou, school of Mathematics and Statistics, the University of Melbourne, Australia
Place: Room 801, the management building
Time: 10:30 a.m. —11:30 a.m. August 27
Abstract:
Let Γ be an undirected graph and e a positive integer. A perfect e-code in Γ is a subset C of V(Γ) such that the closed e-neighbourhoods of the vertices in C form a partition of V(Γ) . Given a finite group G and an inverse-closed subset S of G excluding the identity element, the Cayley graph Cay(G, S) is the graph with vertex set G such that x, y ∈ G are adjacent if and only if yx^{-1} ∈ S. Perfect codes in Cayley graphs can be considered as generalizations of perfect codes in classical coding theory, and perfect 1-codes in Cayley graphs are closely related to tilings of the underlying groups. I will review some of the recent results on perfect codes in Cayley graphs with a focus on perfect 1-codes.
