On perfect codes in Cartesian product of graphs

Michel Mollard (1)

1 IF - Institut Fourier

Assuming the existence of a partition in perfect codes of the vertex set of a finite or infinite bipartite graph $G$ we give the construction of a perfect code in the Cartesian product $ G \Box G \Box P_2$. Such a partition is easily obtained in the case of perfect codes in Abelian Cayley graphs and we give some example of applications of this result and its generalizations.

Mots clés: Graph; Perfect codes; Cartesian Product

Domaines: Combinatoire [math.CO]

Michel Mollard. On perfect codes in Cartesian product of graphs. European Journal of Combinatorics, 2011, 32 (3), pp.398-403. ⟨hal-00535682⟩