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This paper concerns the domination numbers k;n for the complete k n grid graphs for 1 k 10 and n 1. These numbers were previously established for 1 k 4. Here we present dominating sets for 5 k 10 and n 1. This gives upper bounds for k;n for k in this range. We discuss evidence that indicates that these upper bounds are also lower bounds. A dominating set in… (More)
The k n grid graph is the product P k P n of a path of length k ?1 and a path of length n ?1. We prove here formulas found by E. O. Hare for the domination numbers of P 5 P n and P 6 P n .