General bounds on limited broadcast domination

Abstract

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.

18 pages, 8 figures

Cited by in corpus (2)

• 2-limited broadcast domination on grid graphs
• Proving exact values for the $2$-limited broadcast domination number on grid graphs