k-TUPLE DOMATIC IN GRAPHS

For every positive integer k, a set S of vertices in a graph G = (V, E) is a k-tuple dominating set of G if every vertex of V − S is adjacent to at least k vertices and every vertex of S is adjacent to at least k−1 vertices in S. The minimum cardinality of a k-tuple dominating set of G is the k-tuple domination number of G. When k = 1, a k-tuple domination number is the well-studied domination number. We define the k-tuple domatic number of G as the largest number of sets in a partition of V into k-tuple dominating sets. Recall that when k = 1, a k-tuple domatic number is the well-studied domatic number. In this study, basic properties and bounds for the k-tuple domatic number are derived.