## Figures and Tables from this paper

## 10 Citations

Asymptotically Optimal Bounds for (t,2) Broadcast Domination on Finite Grids

- Mathematics
- 2018

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

- Mathematics
- 2017

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

- Mathematics
- 2019

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

- Mathematics
- 2018

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

- Computer Science
- 2019

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.

Efficient (t, r) broadcast dominating sets of the triangular lattice

- MathematicsDiscret. Appl. Math.
- 2020

On $(t,r)$ broadcast domination of directed graphs

- Mathematics
- 2021

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

- Mathematics
- 2020

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.

The (t, r) broadcast domination number of some regular graphs

- MathematicsDiscret. Appl. Math.
- 2021

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A broadcast on a graph G is a function f : V (G) ! f0;1;:::;diam(G)g such that for every vertex v 2 V (G), f(v) e(v), where diam(G) is the diameter of G, and e(v) is the eccentricity of v. In…

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