Note: On the 2-rainbow domination in graphs
Discrete Applied Mathematics
2-rainbow domination of generalized Petersen graphs P(n,2)
Discrete Applied Mathematics
Note: 2-rainbow domination in generalized Petersen graphs P(n,3)
Discrete Applied Mathematics
Discrete Applied Mathematics
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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 v@?V with f(v)=0@?, then f is called a k-rainbow dominating function (kRDF) of G where N(v)={u@?V|uv@?E}. The weight of f, denoted by w(f), is defined as w(f)=@?"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. Bres@?ar and S@?umenjak (2007) [5] gave an upper bound and a lower bound for @c"r"2(GP(n,k)). They showed that @?4n5@?==4k+1.