Optimal (t, r) broadcasts on the infinite grid

@article{Drews2019OptimalR,
  title={Optimal (t, r) broadcasts on the infinite grid},
  author={Benjamin F. Drews and Pamela E. Harris and Timothy W. Randolph},
  journal={Discret. Appl. Math.},
  year={2019},
  volume={255},
  pages={183-197}
}
Asymptotically Optimal Bounds for (t,2) Broadcast Domination on Finite Grids
Let $G=(V,E)$ be a graph and $t,r$ be positive integers. The \emph{signal} that a tower vertex $T$ of signal strength $t$ supplies to a vertex $v$ is defined as $sig(T,v)=max(t-dist(T,v),0),$ where
Computing upper bounds for optimal density of $(t,r)$ broadcasts on the infinite grid
The domination number of a finite graph $G$ with vertex set $V$ is the cardinality of the smallest set $S\subseteq V$ such that for every vertex $v\in V$ either $v\in S$ or $v$ is adjacent to a
(t,r) broadcast domination in the infinite grid
The $(t,r)$ broadcast domination number of a graph $G$, $\gamma_{t,r}(G)$, is a generalization of the domination number of a graph. $\gamma_{t,r}(G)$ is the minimal number of towers needed, placed on
Broadcast Domination of Triangular Matchstick Graphs and the Triangular Lattice
Blessing, Insko, Johnson and Mauretour gave a generalization of the domination number of a graph $G=(V,E)$ called the $(t,r)$ broadcast domination number which depends on the positive integer
Bounds On $(t,r)$ Broadcast Domination of $n$-Dimensional Grids
TLDR
Some upper and lower bounds on the density of a dominating pattern of an infinite grid, as well as methods of computing them are described.
The general position number of integer lattices
On $(t,r)$ broadcast domination of directed graphs
A dominating set of a graph G is a set of vertices that contains at least one endpoint of every edge on the graph. The domination number of G is the order of a minimum dominating set of G. The (t, r)
Projects in (t, r) Broadcast Domination
TLDR
This study focuses on (t, r) broadcast domination, a variant with a connection to the placement of cellphone towers, where some vertices send out a signal to nearby vertices and where all vertices must receive a minimum predetermined amount of this signal.

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