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Given a graph $G$, a dominating set is a set of vertices $D$ such that every vertex of $G$ is in $D$ or adjacent to a vertex in $D$.
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Independent domination number for grid graphs
The independent domination number of grid graphs is known. You can find what you are looking for in the following paper.
S. Crevals and P.R.J. Ostergard, Independent domination of grids, Discrete Mat …