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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2016

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 $\gamma_{p,k}(G-e)$, $\gamma_{p,k}(G/e)$ 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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Dates and versions

hal-01207482 , version 1 (30-09-2015)
hal-01207482 , version 2 (22-02-2016)
hal-01207482 , version 3 (21-03-2016)

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Paul Dorbec, Seethu Varghese, Ambat Vijayakumar. Heredity for generalized power domination. Discrete Mathematics and Theoretical Computer Science, 2016, Vol. 18 no. 3, ⟨10.46298/dmtcs.1290⟩. ⟨hal-01207482v3⟩

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