Bounds On (t,r) Broadcast Domination of n-Dimensional Grids release_junamkx4ibfbfigmu5pygogswq

by Tom Shlomi

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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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Date   2020-02-26
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arXiv  1908.07586v3
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