Kevin R. Hutson1, Stephen T. Hedetniemi1, Richard Forrester2
1Furman University Professor Emeritus Greenville, SC 29613 Clemson University
2 Dickinson College Carlisle, PA 17013
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 \( m \geq 16 \) 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.

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