Abstract:
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 show that γ(Q15) = γ(Q16) = 9 ,
confirm that γ(Q17) = γ(Q18) = 9, show that γ(Q19) = 10, show that i(Q18) = 10,
improve the bound for i(Q19) to 10 ≤ i(Q19) ≤ 11, show that ir(Qn) = γ(Qn) for
1 ≤ n ≤ 13, show that IR(Q9) = Γ(Q9) = 13 and that IR(Q10) = Γ(Q10) = 15, show
that γ(Q4k+1) = 2k +1 for 16 ≤ k ≤ 21, improve the bound for i(Q22) to i(Q22) ≤ 12,
and show that IR(K8) = 17, IR(K9) = 25, IR(K10) = 27, and IR(K11) = 36.