A tight upper bound for 2-rainbow domination in generalized Petersen graphs

Let f be a function that assigns to each vertex a subset of colors chosen from a set C={1,2,...,k} of k colors. If @?"u"@?"N"("v")f(u)=C for each vertex [email protected]?V with f(v)[email protected]?, then f is called a k-rainbow dominating function (kRDF) of G where N(v)={[email protected]?V|[email protected]?E}. The weight of f, denoted by w(f), is defined as w(f)[email protected]?"v"@?"V|f(v)|. Given a graph G, the minimum weight among all weights of kRDFs, denoted by @c"r"k(G), is called the k-rainbow domination number of G. [email protected]?ar and [email protected]?umenjak (2007) [5] gave an upper bound and a lower bound for @c"r"2(GP(n,k)). They showed that @[email protected]?=