Heredity for generalized power domination
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 γ\p,k(G-e), γ\p,k(G/e) and for γ\p,k(G-v) in terms of γ\p,k(G), and give examples for which these bounds are tight. We characterize all graphs for which γ\p,k(G-e) = γ\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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