2-limited broadcast domination on grid graphs

We establish upper and lower bounds for the 2-limited broadcast domination number of various grid graphs, in particular the Cartesian product of two paths, a path and a cycle, and two cycles. The upper bounds are derived by explicit constructions. The lower bounds are obtained via linear programming...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Slobodin, Aaron, MacGillivray, Gary, Myrvold, Wendy
Format: Article
Language:English
Subjects:
Cartesian coordinates
Graphs
Linear programming
Lower bounds
Upper bounds
Online Access:Get full text
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Summary:We establish upper and lower bounds for the 2-limited broadcast domination number of various grid graphs, in particular the Cartesian product of two paths, a path and a cycle, and two cycles. The upper bounds are derived by explicit constructions. The lower bounds are obtained via linear programming duality by finding lower bounds for the fractional 2-limited multipacking numbers of these graphs.
ISSN:2331-8422
DOI:10.48550/arxiv.2110.08938