Title: The relationship between $k$-forcing and $k$-power domination,
Abstract: Zero forcing and power domination are iterative processes on graphs where an
initial set of vertices are observed, and additional vertices become observed
based on some rules. In both cases, the goal is to eventually observe the
entire graph using the fewest number of initial vertices. Chang et al.
introduced $k$-power domination in [Generalized power domination in graphs,
{\it Discrete Applied Math.} 160 (2012) 1691-1698] as a generalization of power
domination and standard graph domination. Independently, Amos et al. defined
$k$-forcing in [Upper bounds on the $k$-forcing number of a graph, {\it
Discrete Applied Math.} 181 (2015) 1-10] to generalize zero forcing. In this
paper, we combine the study of $k$-forcing and $k$-power domination, providing
a new approach to analyze both processes. We give a relationship between the
$k$-forcing and the $k$-power domination numbers of a graph that bounds one in
terms of the other. We also obtain results using the contraction of subgraphs
that allow the parallel computation of $k$-forcing and $k$-power dominating
sets.