Proving exact values for the 2-limited broadcast domination number on
grid graphsArticle
Authors: Aaron Slobodin ; Gary MacGillivray ; Wendy Myrvold
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Aaron Slobodin;Gary MacGillivray;Wendy Myrvold
We establish exact values for the 2-limited broadcast domination number of
various grid graphs, in particular Cm◻Cn for 3≤m≤6 and
all n≥m, Pm◻C3 for all m≥3, and Pm◻Cn for
4≤m≤5 and all n≥m. We also produce periodically optimal
values for Pm◻C4 and Pm◻C6 for m≥3, P4◻Pn for n≥4, and P5◻Pn for n≥5. Our method completes
an exhaustive case analysis and eliminates cases by combining tools from linear
programming with various mathematical proof techniques.