On the $$\varvec{k}$$ k -power domination of hypergraphs

Abstract

The study of electric power networks led to the definition and study of power domination in graphs. This notion was later extended to k-power domination. In the current paper we start the study of the k-power domination in hypergraphs. In particular, we give a structural characterization of the k-power domination number for hypertrees. We also establish a linear-time algorithm to solve the k-power domination problem in hypertrees. Finally, lower and upper bounds for the k-power domination number of standard and non standard connected (r-uniform) hypergraphs are obtained.