2016/09/13 by He Huang, Huang, He, Binzhou Xia +3 · 4 citations
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1609.03755
openalex publication_date 2016/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a graph Γ, a subset C of V(Γ) is called a perfect code in Γ if every vertex of Γ is at distance no more than one to exactly one vertex in C, and a subset C of V(Γ) is called a total perfect code in Γ if every vertex of Γ is adjacent to exactly one vertex in C. In this paper we study perfect codes and total perfect codes in Cayley graphs, with a focus on the following themes: when a subgroup of a given group is a (total) perfect code in a Cayley graph of the group; and how to construct new (total) perfect codes in a Cayley graph from known ones using automorphisms of the underlying group. We prove several results around these questions.