مشخصات پژوهش

Abstract. 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 f1; 2g such that for any vertex v 2 V with f(v) = ∅ the condition ∪u2N(v) f(u) = f1; 2g is fullled. A 2RDF f is independent (I2RDF) if no two vertices assigned nonempty sets are adjacent. The weight of a 2RDF f is the value !(f) = Σv2V jf(v)j. The 2-rainbow domination number r2(G) (respectively, the independent 2-rainbow domination number ir2(G) ) is the minimum weight of a 2RDF (respectively, I2RDF) on G. We say that r2(G) is strongly equal to ir2(G) and denote by r2(G)  ir2(G), if every 2RDF on G of minimum weight is an I2RDF. In this paper we characterize all unicyclic graphs G with r2(G)  ir2(G).