General bounds on limited broadcast domination
  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. 
Jos\'e C\'aceres, Carmen Hernando, Merc\`e Mora, Ignacio M. Pelayo,   Mar\'ia Luz Puertas
math.CO