A perfect code in a graph Γ= (V, E) is a subset C of V such that no two vertices in C are adjacent and every vertex in V C is adjacent to exactly one vertex in C. A total perfect code in Γ is a subset C of V such that every vertex of 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.
Cameron et al. (Wed,) studied this question.
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