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arXiv · 1410.4149

New Upper Bounds on the Distance Domination Numbers of Grids

Armando Grez·Michael Farina
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Abstract

In his 1992 Ph.D. thesis Chang identified an efficient way to dominate $m \times n$ grid graphs and conjectured that his construction gives the most efficient dominating sets for relatively large grids. In 2011 Gonçalves, Pinlou, Rao, and Thomassé proved Chang's conjecture, establishing a closed formula for the domination number of a grid. In March 2013 Fata, Smith and Sundaram established upper bounds for the $k$-distance domination numbers of grid graphs by generalizing Chang's construction of dominating sets to $k$-distance dominating sets. In this paper we improve the upper bounds established by Fata, Smith, and Sundaram for the $k$-distance domination numbers of grids.

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Armando Grez, Michael Farina. 2014-10-15. New Upper Bounds on the Distance Domination Numbers of Grids. https://arxiv.org/abs/1410.4149

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