Minimum Size of dominating set of n*n table

Question

What is the minimum size of dominating set of $N*N$ table graph? $N*N$ table graph definition: Consider each cell of table a vertex and connect vertex v and vertex u when cell v and cell u is adjacent in table.

Answer 1

I think that https://arxiv.org/abs/1102.5206 answer this. Unfortunatley, stackexchange seems to require answers with at least 30 characters, which is the reason for this second sentence.