Computational methods and new results for chessboard problems

We describe various computing techniques for tackling chessboard domination problems and apply these to the determination of domination and irredundance numbers for queens' and kings' graphs. In particular we confirm that "((QI7) = "((QI8) = 9, and show that "((Q14) = 8, ')'(QI5) "((Q16) = 9, ')'(QI9) = 10, i(QI8) = 10, 10 ::; i(Q19) ::; 11, ir(Qn) = "((Qn) for 1 ::; n ::; 13, IR(Q9) = r(Q9) = 13, IR(QlO) = r(QlO) = 15, ')'(Q4k+d = 2k + 1 for k = 16,18,20 and 21, i(Q22) ::; 12, I R(Ks) = 17, I R(K9) = 25, I R(KlO) = 27, and I R(Kl1 ) = 36. We calculate the number of non-isomorphic minimum dominating and independent dominating sets in the queens' graph Qn for n ::; 15 and n ::; 18 respectively.

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