Domination in the generalized Petersen graph P(ck, k)

Let G = (V, E) be a graph. A subset S C V is a dominating set of G, if every vertex u is an element of V - S is dominated by some vertex v is an element of S. The domination number, denoted by gamma(G), is the minimum cardinality of a dominating set. Determining the domination number of a graph G is an NP-complete problem, and only for few families of graphs, the exact domination number is known. In this paper, we study the domination number for the generalized Petersen graph P(ck, k), where c >= 3 is a constant. We obtain upper bound on gamma(P(ck, k)) for general c. We also show that gamma(P(3k,k)) =[-5k/3] for any k >= 1, and gamma(P(4k, k)) = 2k for odd k.