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arXiv · 1710.05953

Dominating 2-broadcast in graphs: complexity, bounds and extremal graphs

José Cáceres·Carmen Hernando·Mercè Mora·Ignacio M. Pelayo·María Luz Puertas
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Abstract

Limited dominating broadcasts were proposed as a variant of dominating broadcasts, where the broadcast function is upper bounded. As a natural extension of domination, we consider dominating $2$-broadcasts along with the associated parameter, the dominating $2$-broadcast number. We prove that computing the dominating $2$-broadcast number is a NP-complete problem, but can be achieved in linear time for trees. We also give an upper bound for this parameter, that is tight for graphs as large as desired.

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José Cáceres, Carmen Hernando, Mercè Mora, Ignacio M. Pelayo, María Luz Puertas. 2017-10-16. Dominating 2-broadcast in graphs: complexity, bounds and extremal graphs. https://arxiv.org/abs/1710.05953

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