On the domination number of Hamiltonian graphs with minimum degree six

Let G=(V,E)G=(V,E) be a simple graph. A set D⊆VD⊆V is a dominating set   of GG if every vertex of V−DV−D is adjacent to a vertex of DD. The domination number   of GG, denoted by γ(G)γ(G), is the minimum cardinality of a dominating set of GG. We prove that if GG is a Hamiltonian graph of order nn with minimum degree at least six, then γ(G)≤6n17.