The Domination Number of Grids

TL;DR

This paper determines the exact domination number for all grid graphs of size n by m, confirming a conjecture that provides a simple formula for these values.

Contribution

It proves Chang's conjecture, establishing a closed-form formula for the domination number of all n by m grid graphs for n,m ≥ 16.

Findings

Confirmed the formula for domination number of grid graphs

Proved Chang's conjecture for all n,m ≥ 16

Provided a complete characterization of domination numbers in grid graphs

Abstract

In this paper, we conclude the calculation of the domination number of all $n\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\le n\le m$, $\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4$.