Optimal \((t, r)\) broadcasts on the infinite grid

DOI10.1016/j.dam.2018.08.009zbMath1405.05133arXiv1711.11116OpenAlexW2963993275MaRDI QIDQ1727739

Timothy W. Randolph, Benjamin F. Drews, Pamela E. Harris

Publication date: 20 February 2019

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.11116

zbMATH Keywords

dominationgrid graphsbroadcasts

Mathematics Subject Classification ID

Small world graphs, complex networks (graph-theoretic aspects) (05C82) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items

The general position number of integer lattices ⋮ Bounds On $(t,r)$ Broadcast Domination of $n$-Dimensional Grids ⋮ Projects in (t, r) Broadcast Domination ⋮ The \(( t , r )\) broadcast domination number of some regular graphs ⋮ Efficient \(( t , r )\) broadcast dominating sets of the triangular lattice ⋮ trb.py ⋮ Perfect domination ratios of Archimedean lattices

Uses Software

• GitHub

Cites Work

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• Relations between packing and covering numbers of a tree
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• R -Domination in Graphs
• New Upper Bounds on the Distance Domination Numbers of Grids
• The domination numbers of the 5 × n and 6 × n grid graphs
• Broadcast Domination in Tori