Let k ≥ 1 be an integer, and let D = (V; A) be a finite simple digraph, for which d D − ≥ k − 1 for all v ɛ V. A function f: V → {−1; 1} is called a signed k-dominating function (SkDF) if f(N −[v]) ≥ k for each vertex v ɛ V. The weight w(f) of f is defined by . The signed k-domination number for a digraph D is γ kS (D) = min {w(f|f) is an SkDF of D. In this paper, we initiate the study of signed k-domination in digraphs. In particular, we present some sharp lower bounds for γ kS (D) in terms of the order, the maximum and minimum outdegree and indegree, and the chromatic number. Some of our results are extensions of well-known lower bounds of the classical signed domination numbers of graphs and digraphs.
