2020/07/16 by Xuanlong Ma, Ma, Xuanlong, Kaishun Wang +3 · 2 citations
Computer Science · Engineering · #05C25 #05C69 #94B25 #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2007.08163
openalex publication_date 2020/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A subset C of the vertex set of a graph Γ is called a perfect code of Γ if every vertex of Γ is at distance no more than one to exactly one vertex in C. Let A be a finite abelian group and T a square-free subset of A. The Cayley sum graph of A with respect to the connection set T is a simple graph with A as its vertex set, and two vertices x and y are adjacent whenever x+y∈ T. A subgroup of A is said to be a subgroup perfect code of A if the subgroup is a perfect code of some Cayley sum graph of A. In this paper, we give some necessary and sufficient conditions for a subset of A to be a perfect code of a given Cayley sum graph of A. We also characterize all subgroup perfect codes of A.