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Monchaya Chiangpradit, Passawan Noppakaew, Sawanya Sakuntasathien, Natwarat Sanguanphanich, Kanisorn Sawangtong,
Upper bounds of k-Limited Dominating Broadcasts for Some Grid Graphs.
Int. J. Math. Comput. Sci., 20, no. 1, (2025), 151-156

DOI:

https://doi.org/10.69793/ijmcs/01.2025/chiangpradit

Keywords and phrases:

Broadcast, dominating broadcast, broadcast domination number, k-limited broadcast.

Abstract:

A broadcast domination is a structure that combines classical domination and broadcasting formation. In order to design a broadcast scheme with limited capacity, the concept of k-limited broadcast domination is of interest. In this work, we show that a grid graph of dimension nxm can have a 3-limited broadcast with only one broadcast vertex if and only if \lfloor{\frac{n}{2}}\rfloor + \lfloor{\frac{m}{2}}\rfloor \leq k. In addition, we provide its upper bound for 3-limited broadcast domination number.