2025/07/16 by Cameron, Peter J., Yap, Roro Sihui, Zhou, Sanming · 1 citation
#05C25 #05C69 #94B25 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2507.11871
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.