Abstract
The concept of 2-rainbow domination of a graph G coincides with the ordinary domination of the prism G □ K 2 . 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 ⌈ 4 n / 5 ⌉ and n with both bounds being sharp.
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