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

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arxiv 1710.05953 v1 pith:PY4265Y6 submitted 2017-10-16 math.CO

José Cáceres , Carmen Hernando , Mercè Mora , Ignacio M. Pelayo , María Luz Puertas This is my paper
classification math.CO
keywords dominatingbroadcastbroadcastsgraphsnumberparameterupperachieved
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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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