Constructing $\gamma$-Sets of Grids

Abstract

A lot of research has been spent determining the domination numbers, ${\gamma }_{m,n}$, of grid graphs. But relatively little effort has been given to constructing minimum dominating sets of grid graphs. In this paper, we introduce a method for constructing $\gamma$-sets of grid graphs $G_{m,n}$ for all $m\ge 16$ and $n\ge 16$. Further, for $G_{m,n}$, $m<16$, $m\ne 12,13$, we show how particular $\gamma$-sets can be used to construct $\gamma$-sets for other grid graphs.