Properties of dominating sets of the queens graph Q4k+3 - Burger A.P.; Mynhardt C.M. (Utilitas Mathematica, 2000)
he domination number γ(Qn) of the queens graph Qn is the minimum number of queens required to cover every square on an n×n chessboard. We discuss properties of dominating sets of Q4k+3 of cardinality 2k+1 and show that such sets do not exist for 3 ≤ k ≤ 7. This result yields the new domination numbers γ(Q19) = 10 and γ (Q31) = 16.