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Bounds on the k-tuple domatic number of a graph

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A vertex of a graph G dominates itself and all vertices adjacent to it. A subset S ⊆ V (G) is a k-tuple dominating set of G if each vertex of V (G) is dominated by at least k vertices in S. The k-tuple domatic number of G is the largest number of sets in a partition of V (G) into k-tuple dominating sets.In this paper, we present a lower bound on the k-tuple domatic number, and we establish Nordhaus-Gaddum inequalities. Some of our results extends those for the classical domatic number.