Proving exact values for the $2$-limited broadcast domination number on grid graphs

Abstract

We establish exact values for the $2$-limited broadcast domination number of various grid graphs, in particular $C_m\square C_n$ for $3\le m\le 6$ and all $n\ge m$, $P_m\square C_3$ for all $m\ge 3$, and $P_m\square C_n$ for $4\le m\le 5$ and all $n\ge m$. We also produce periodically optimal values for $P_m\square C_4$ and $P_m\square C_6$ for $m\ge 3$, $P_4\square P_n$ for $n\ge 4$, and $P_5\square P_n$ for $n\ge 5$. Our method completes an exhaustive case analysis and eliminates cases by combining tools from linear programming with various mathematical proof techniques.

References in corpus (1)

• 2-limited broadcast domination on grid graphs