Geodesic
Proving exact values for the $2$-limited broadcast domination number on grid graphs
Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 2.

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We establish exact values for the $2$-limited broadcast domination number of various grid graphs, in particular $C_m\square C_n$ for $3 \leq m \leq 6$ and all $n\geq m$, $P_m \square C_3$ for all $m \geq 3$, and $P_m \square C_n$ for $4\leq m \leq 5$ and all $n \geq m$. We also produce periodically optimal values for $P_m \square C_4$ and $P_m \square C_6$ for $m \geq 3$, $P_4 \square P_n$ for $n \geq 4$, and $P_5 \square P_n$ for $n \geq 5$. Our method completes an exhaustive case analysis and eliminates cases by combining tools from linear programming with various mathematical proof techniques.
DOI : 10.46298/dmtcs.11478
Classification : 05C69, 90C05 
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     title = {Proving exact values for the $2$-limited broadcast domination number on grid graphs},
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Slobodin, Aaron; MacGillivray, Gary; Myrvold, Wendy. Proving exact values for the $2$-limited broadcast domination number on grid graphs. Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 2. doi : 10.46298/dmtcs.11478. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.11478/

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