Computing the domination number of grid graphs

Abstract

Let γm,n denote the size of a minimum dominating set in the m× n grid graph. For the square grid graph, exact values for γn,n have earlier been published for n ≤ 19. By using a dynamic programming algorithm, the values of γm,n for m, n ≤ 29 are here obtained. Minimum dominating sets for square grid graphs up to size 29 × 29 are depicted.