## José Cáceres ; Carmen Hernando ; Mercè Mora ; Ignacio M. Pelayo ; María Luz Puertas - General bounds on limited broadcast domination

dmtcs:4054 - Discrete Mathematics & Theoretical Computer Science, October 29, 2018, vol. 20 no. 2 - https://doi.org/10.23638/DMTCS-20-2-13
General bounds on limited broadcast domination

Authors: José Cáceres ; Carmen Hernando ; Mercè Mora ; Ignacio M. Pelayo ; María Luz Puertas

Dominating broadcasting is a domination-type structure that models a transmission antenna network. In this paper, we study a limited version of this structure, that was proposed as a common framework for both broadcast and classical domination. In this limited version, the broadcast function is upper bounded by an integer $k$ and the minimum cost of such function is the dominating $k$-broadcast number. Our main result is a unified upper bound on this parameter for any value of $k$ in general graphs, in terms of both $k$ and the order of the graph. We also study the computational complexity of the associated decision problem.

Volume: vol. 20 no. 2
Section: Graph Theory
Published on: October 29, 2018
Accepted on: October 29, 2018
Submitted on: November 7, 2017
Keywords: Mathematics - Combinatorics,05C69

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