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Aaron Slobodin ; Gary MacGillivray ; Wendy Myrvold - Proving exact values for the 2-limited broadcast domination number on grid graphs

dmtcs:11478 - Discrete Mathematics & Theoretical Computer Science, November 22, 2023, vol. 25:2 - https://doi.org/10.46298/dmtcs.11478
Proving exact values for the 2-limited broadcast domination number on grid graphsArticle

Authors: Aaron Slobodin ; Gary MacGillivray ; Wendy Myrvold

    We establish exact values for the 2-limited broadcast domination number of various grid graphs, in particular CmCn for 3m6 and all nm, PmC3 for all m3, and PmCn for 4m5 and all nm. We also produce periodically optimal values for PmC4 and PmC6 for m3, P4Pn for n4, and P5Pn for n5. Our method completes an exhaustive case analysis and eliminates cases by combining tools from linear programming with various mathematical proof techniques.


    Volume: vol. 25:2
    Section: Graph Theory
    Published on: November 22, 2023
    Accepted on: October 6, 2023
    Submitted on: June 16, 2023
    Keywords: Mathematics - Combinatorics
    Funding:
      Source : OpenAIRE Graph
    • Funder: Natural Sciences and Engineering Research Council of Canada

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