On the domination number of Hamiltonian graphs with minimum degree six

Abstract Let G = ( V , E ) be a simple graph. A set D ⊆ V is a dominating set of G if every vertex of V − D is adjacent to a vertex of D . The domination number of G , denoted by γ ( G ) , is the minimum cardinality of a dominating set of G . We prove that if G is a Hamiltonian graph of order n with minimum degree at least six, then γ ( G ) ≤ 6 n 17 .