مشخصات پژوهش

A 2-rainbow dominating function (2RDF) of a graph G is a function f from the vertex set V (G) to the set of all subsets of the set {1, 2} such that for any vertex v ∈ V (G) with f(v) = ∅, the condition Su∈N(v) f(u) = {1, 2} is fulfilled. The weight of a 2RDF f is the value ω(f) = Pv∈V (G) |f(v)|. The 2-rainbow domination number of a graph G, denoted by γr2(G), is the minimum weight of a 2RDF of G. The rainbow bondage number br2(G) of a graph G with maximum degree at least two is the minimum cardinality of all sets E ⊆ E(G) for which γr2(G − E) > γr2(G). Dehgardi, Sheikholeslami and Volkmann, [The k-rainbow bondage number of a graph, 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 generalize their result for graphs which admit a 2-cell embedding on a surface with non-negative Euler characteristic.