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Abstract
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Let k be a positive integer, and set [k] := f1, 2, . . . , kg. For a graph G, a k-rainbow dominating
function (or kRDF) of G is a mapping f : V(G) ! 2[k] in such a way that, for any vertex v 2 V(G)
with the empty set under f , the condition
S
u2NG(v) f (u) = [k] always holds, where NG(v) is the open
neighborhood of v. The weight of kRDF f of G is the summation of values of all vertices under f .
The k-rainbow domination number of G, denoted by grk(G), is the minimum weight of a kRDF of G.
In this paper, we obtain the k-rainbow domination number of grid P3Pn for k 2 f2, 3, 4g.
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