The exact domination number of the generalized Petersen graphs

Let G = ( V , E ) be a graph. A subset S ⊆ V is a dominating set of G , if every vertex u ∈ V − S is dominated by some vertex v ∈ S . The domination number, denoted by γ ( G ) , is the minimum cardinality of a dominating set. For the generalized Petersen graph 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 ) ) ≤ ⌈ 3 n 5 ⌉ and conjectured that the upper bound ⌈ 3 n 5 ⌉ is the exact domination number. In this paper we prove this conjecture.