2-Rainbow Domination Number of Some Graphs

A 2-rainbow domination function of a graph G is a function f that assigns to each vertex a set ofcolors chosen from the set {1,2}, such that for any ? ∈ ?(?), ?(?) = ∅ implies ⋃?∈?(?) |?(?)| ={1,2}. The 2-rainbow domination number ??2(?) of a graph G is minimum w(?) = Σ?∈?(?) |?(?)|over all such functions f. In this paper, we show that upper bounds of 2-rainbow dominationnumbers of several classes of graphs.

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