We determine upper bounds for $γ(Qn^t)$ and $i(Qₙ^t)$, the domination and independent domination numbers, respectively, of the graph $Qₙ^t$ obtained from the moves of queens on the n×n chessboard drawn on the torus.
[13] P.R.J. Östergå rd and W.D. Weakley, Values of domination numbers of the queen's graph, Electron. J. Combin. 8 (2001) no. 1, Research paper 29, 19 pp.
[14] W.D. Weakley, Domination In The Queen's Graph, in: Y. Alavi and A.J. Schwenk, eds, Graph Theory, Combinatorics, and Algorithms, Volume 2, pages 1223-1232 (Wiley-Interscience, New York, 1995).
[15] W.D. Weakley, A lower bound for domination numbers of the queen's graph, J. Combin. Math. Combin. Comput., to appear.
[16] W.D. Weakley, Upper bounds for domination numbers of the queen's graph, Discrete Math. 242 (2002) 229-243, doi:10.1016/S0012-365X(00)00467-2.