  In this paper, we study the behaviour of the generalized power domination
number of a graph by small changes on the graph, namely edge and vertex
deletion and edge contraction. We prove optimal bounds for
$\gamma\_{p,k}(G-e)$, $\gamma\_{p,k}(G/e)$ and for $\gamma\_{p,k}(G-v)$ in
terms of $\gamma\_{p,k}(G)$, and give examples for which these bounds are
tight. We characterize all graphs for which $\gamma\_{p,k}(G-e) =
\gamma\_{p,k}(G)+1$ for any edge $e$. We also consider the behaviour of the
propagation radius of graphs by similar modifications.
