The Rainbow Domination Number of a Digraph
نویسندگان
چکیده
Let D = (V,A) be a finite and simple digraph. A II-rainbow dominating function (2RDF) of a digraph D is a function f from the vertex set V to the set of all subsets of the set {1, 2} such that for any vertex v ∈ V with f(v) = ∅ the condition ⋃ u∈N−(v) f(u) = {1, 2} is fulfilled, where N−(v) is the set of in-neighbors of v. The weight of a 2RDF f is the value ω(f) = ∑ v∈V |f(v)|. The 2-rainbow domination number of a digraph D, denoted by γr2(D), is the minimum weight of a 2RDF of D. In this paper we initiate the study of rainbow domination in digraphs and we present some sharp bounds for γr2(D).
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