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Perfect codes in Cayley graphs

Series: Department Seminar

Speaker: Prof. Sanming Zhou, School of Mathematics and Statistics, The University of Melbourne, Australia

Date/Time: Dec 22 15:00:00

Location: CSA Seminar Hall (Room No. 254, First Floor)

Abstract:
For a graph $Gamma$ and a positive integer $e$, a perfect $e$-code in $Gamma$ is a subset $C$ of $V(Gamma)$ such that the closed $e$-neighbourhoods of the vertices in $C$ form a partition of $V(Gamma)$. Given a finite group $G$ and an inverse-closed subset $S$ of $G$ excluding the identity element, the Cayley graph $mathrm{Cay}(G, S)$ is the graph with vertex set $G$ such that $x, y in G$ are adjacent if and only if $yx^{-1} in S$. Perfect codes in Cayley graphs can be considered as generalisations of perfect codes in classical coding theory, and perfect $1$-codes in Cayley graphs are closely related to tilings of the underlying groups.

Host Faculty: Prof. Sunil L Chandran