An improved upper bound for queens domination numbers Original Research Article

We consider the domination number of the queens graph Qn and show that if, for some fixed k, there is a dominating set of Q4k+1 of a certain type with cardinality 2k+1, then for any n large enough, γ(Qn)⩽[(3k+5)/(6k+3)]n+O(1). The same construction shows that for any m⩾1 and n=2(6m−1)(2k+1)−1, γ(Qnt)⩽[(2k+3)/(4k+2)]n+O(1), where Qnt is the toroidal n×n queens graph.