مشخصات پژوهش

A 2-rainbow dominating function (2RDF) on a graph G = (V, E) 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 conditionu∈N(v) f (u) = {1, 2} is fulfilled.A2RDF f is independent (I2RDF) if no two vertices assigned nonempty sets are adjacent. The weight of a 2RDF f is the value ω( f ) = v∈V | f (v)|. The 2-rainbow domination number γr2(G) (respectively, the independent 2-rainbow domination number ir2(G)) is the minimum weight of a 2RDF (respectively, I2RDF) on G. We say that γr2(G) is strongly equal to ir2(G) and denote by γr2(G) ≡ ir2(G), if every 2RDF on G of minimumweight is an I2RDF. In this paper,we provide a constructive characterization of trees T with γr2(T ) ≡ ir2(T ).