2-Rainbow domination number of Cn□C5Cn□C5

In this paper we prove that γr2(Cn□C5)≥2nγr2(Cn□C5)≥2n. This, together with the result of Stȩpień and Zwierzchowski (2014), gives γr2(Cn□C5)=2nγr2(Cn□C5)=2n. Since for n=5kn=5k we have γ(Cn□C5)=nγ(Cn□C5)=n (see Klavžar and Seifter (1995)), it follows that a product Cn□C5Cn□C5 is an example of a graph class for which γr2=2γγr2=2γ. Moreover, Cn□C5Cn□C5 is an example of a graph class for which γw2=γr2γw2=γr2, where γw2γw2 is a weak {2}-domination number introduced in Brešar et al. (2008).