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Bounds On (t,r) Broadcast Domination of n-Dimensional Grids
release_junamkx4ibfbfigmu5pygogswq
by
Tom Shlomi
Released
as a article
.
2020
Abstract
In this paper, we study at a variant of graph domination known as (t, r)
broadcast domination, first defined by Blessing, Insko, Johnson, and Mauretour
in 2015. In this variant, each broadcast provides t-d reception to each
vertex a distance d < t from the broadcast. A vertex is considered dominated
if it receives r total reception from all broadcasts. Our main results
provide some upper and lower bounds on the density of a (t, r) dominating
pattern of an infinite grid, as well as methods of computing them. Also, when
r > 2 we describe a family of counterexamples to a generalization of
Vizing's Conjecture to (t,r) broadcast domination.
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1908.07586v3
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