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Proving exact values for the$2$ -limited broadcast domination number on grid graphs
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Proving exact values for the$2$ -limited broadcast domination number on grid graphs
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Journal Article
Proving exact values for the$2$ -limited broadcast domination number on grid graphs
2023
Overview
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.
Publisher
Discrete Mathematics & Theoretical Computer Science
Subject
