The 2-domination and Roman domination numbers of grid graphs
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We investigate the 2-domination number for grid graphs, that is the size of a smallest set D of vertices of the grid such that each vertex of the grid belongs to D or has at least two neighbours in D. We give a closed formula giving the 2-domination number of any n × m grid, hereby confirming the known results (for n ≤ 5). The proof relies on some dynamic programming algorithms, using transfer matrices in (min,+)-algebra We also apply the method to solve the Roman domination problem on grid graphs.
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