مشخصات پژوهش

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.