Computing the domination number of grid graphs (Q553994)

Summary: Let \(\gamma_{m,n}\) denote the size of a minimum dominating set in the \(m \times n\) grid graph. For the square grid graph, exact values for \(\gamma_{n,n}\) have earlier been published for \(n \leqslant 19\). By using a dynamic programming algorithm, the values of \(\gamma _{m,n}\) for \(m,\, n\leqslant 29\) are here obtained. Minimum dominating sets for square grid graphs up to size \(29 \times 29\) are depicted.