Geodesic
General bounds on limited broadcast domination
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 2.

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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. 
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     author = {C\'aceres, Jos\'e and Hernando, Carmen and Mora, Merc\`e and Pelayo, Ignacio M. and Puertas, Mar{\'\i}a Luz},
     title = {General bounds on limited broadcast domination},
     journal = {Discrete mathematics & theoretical computer science},
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     number = {2},
     year = {2018},
     doi = {10.23638/DMTCS-20-2-13},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-2-13/}
}
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Cáceres, José; Hernando, Carmen; Mora, Mercè; Pelayo, Ignacio M.; Puertas, María Luz. General bounds on limited broadcast domination. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 2. doi : 10.23638/DMTCS-20-2-13. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-2-13/

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