Perfect codes in Cayley graphs of abelian groups

期刊论文
出版模式：

开放获取
发表日期：

2026年4月9日

查看全文

Peter J. Cameron,
Roro Sihui Yap,
Sanming Zhou

摘要

A perfect code in a graph $\Gamma = (V, E)$ $Γ = (V, E)$ is a subset C of V such that no two vertices in C are adjacent and every vertex in $V \setminus C$ $V \ C$ is adjacent to exactly one vertex in C. A total perfect code in $\Gamma $ $Γ$ is a subset C of V such that every vertex of $\Gamma $ $Γ$ is adjacent to exactly one vertex in C. In this paper we prove several results on perfect codes and total perfect codes in Cayley graphs of finite abelian groups.