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1 LaBRI - Laboratoire Bordelais de Recherche en Informatique 2 Cochin University of Science and Technology

Abstract : 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.

Keywords : power domination heredity vertex deletion edge deletion edge contraction propagation radius

Author: Paul Dorbec - Seethu Varghese - Ambat Vijayakumar -



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