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Proving exact values for the2 -limited broadcast domination number on grid graphs
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Proving exact values for the2 -limited broadcast domination number on grid graphs
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Journal Article
Proving exact values for the2 -limited broadcast domination number on grid graphs
2023
Overview
We establish exact values for the2 -limited broadcast domination number of various grid graphs, in particularC_(m)□ C_(n)for3 ≤ m ≤ 6and alln≥ m ,P_(m) □ C₃for allm ≥ 3 , andP_(m) □ C_(n)for4≤ m ≤ 5and alln ≥ m . We also produce periodically optimal values forP_(m) □ C₄andP_(m) □ C₆form ≥ 3 ,P₄ □ P_(n)forn ≥ 4 , andP₅ □ P_(n)forn ≥ 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
