Geodesic
Heredity for generalized power domination
Discrete mathematics & theoretical computer science, Tome 18 (2015-2016) no. 3.

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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. 
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     author = {Dorbec, Paul and Varghese, Seethu and Vijayakumar, Ambat},
     title = {Heredity for generalized power domination},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2015-2016},
     doi = {10.46298/dmtcs.1290},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.1290/}
}
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Dorbec, Paul; Varghese, Seethu; Vijayakumar, Ambat. Heredity for generalized power domination. Discrete mathematics & theoretical computer science, Tome 18 (2015-2016) no. 3. doi : 10.46298/dmtcs.1290. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.1290/

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