The concept of 2-rainbow domination of a graph
G coincides with the ordinary domination of the prism
G□K2. In this paper, we show that the problem of deciding if a graph has a 2-rainbow dominating function of a given weight is NP-complete even when restricted to bipartite graphs or chordal graphs. Exact values of 2-rainbow domination numbers of several classes of graphs are found, and it is shown that for the generalized Petersen graphs
GP(n,k) this number is between
4n/5![right ceiling](http://www.sciencedirect.com/scidirimg/entities/2309.gif)
and
n with both bounds being sharp.