The exact domination number of the generalized Petersen graphs

Let G=(V,E)G=(V,E) be a graph. A subset S⊆VS⊆V is a dominating set of GG, if every vertex u∈V−Su∈V−S is dominated by some vertex v∈Sv∈S. The domination number, denoted by γ(G)γ(G), is the minimum cardinality of a dominating set. For the generalized Petersen graph G(n)G(n), Behzad et al. [A. Behzad, M. Behzad, C.E. Praeger, On the domination number of the generalized Petersen graphs, Discrete Mathematics 308 (2008) 603–610] proved that γ(G(n))≤⌈3n5⌉ and conjectured that the upper bound ⌈3n5⌉ is the exact domination number. In this paper we prove this conjecture.