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)) ≤ d 3n 5 e and conjectured that the upper bound d 3n 5 e is the exact domination number. In this paper we prove this conjecture. © 2008 Elsevier B.V. All rights reserved.