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 f1; 2g such that for any vertex v 2 V with f(v) = ; the condition [u2N(v)f(u) = f1; 2g is fullled. The weight of a 2RDF f is the value !(f) = P v2V (G) jf(v)j. The 2-rainbow domination number, denoted by r2(G), is the minimum weight of a 2RDF on G. The rainbow bondage number br2(G) of a graph G with maximum degree at least two, is the minimum cardinality of all sets E0  E(G) for which r2(G 􀀀 E0) > r2(G). Dehgardi, Sheikholeslami and Volkmann, [Discrete Appl. Math. 174 (2014), 133-139] proved that the rainbow bondage number of a planar graph does not exceed 15. In this paper we improve this result.