Heredity for generalized power domination

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 $\gamma \mathrm{\_}p,k(G-e)$, $\gamma \mathrm{\_}p,k(G\mathrm{/}e)$ and for $\gamma \mathrm{\_}p,k(G-v)$ in terms of $\gamma \mathrm{\_}p,k(G)$, and give examples for which these bounds are tight. We characterize all graphs for which $\gamma_{p,k}(G-e) = \gamma_{p,k}(G)+1$foranyedge$e$. We also consider the behaviour of the propagation radius of graphs by similar modifications.