Constructing y-Sets of Grids

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 \( m \geq 16 \) and \( n \geq 16 \). Further, for \( G_{m,n} \), \( m < 16 \), \( m \neq 12, 13 \), we show how particular \( \gamma \)-sets can be used to construct \( \gamma \)-sets for other grid graphs.