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 ∪ u∈N(v) f (u) = {1, 2} is fulfilled. The weight of a 2RDF f is the value ω(f ) = Σ v∈V |f (v )|. The 2-rainbow domination number of a graph G, denoted by γ r2 (G), is the minimum weight of a 2RDF of G. The 2-rainbow domination subdivision number sd γ r2 (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the 2-rainbow domination number. In this paper, we initiate the study of 2-rainbow domination subdivision number in graphs.
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