The k-Rainbow Bondage Number of a Digraph
Let D = (V,A) be a finite and simple digraph. A k-rainbow dominating function (kRDF) of a digraph D is a function f from the vertex set V to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V with f(v) = Ø the condition ∪u∈N−(v) f(u) = {1, 2, . . . , k} is fulfilled, where N−(v) is the set of in-neighbors of v. The weight of a kRDF f is the value w(f) = ∑v∈V |f(v)|. The k-rainbow domination number of a digraph D, denoted by γrk(D), is the minimum weight of a kRDF...