The minus k-domination numbers in digraphs

Let [Formula: see text] be a finite and simple digraph with vertex set [Formula: see text]. For any integer [Formula: see text], a minus [Formula: see text]-dominating function (M[Formula: see text]DF) on a digraph [Formula: see text] is a function [Formula: see text] such that [Formula: see text] for each [Formula: see text]. The weight of an M[Formula: see text]DF [Formula: see text] is [Formula: see text]. The minus [Formula: see text]-domination number [Formula: see text] of [Formula: see text] is the maximum weight of an M[Formula: see text]DF on [Formula: see text]. In this paper, we initiate the study of the minus [Formula: see text]-domination number of digraphs, and we present different bounds on [Formula: see text]. In addition, we determine the minus [Formula: see text]-domination number of some classes of digraphs. Some of our results are extensions of known properties of the minus domination numbers of graphs and digraphs.