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arXiv · 1603.07243

Heredity for generalized power domination

Paul Dorbec·Seethu Varghese·Ambat Vijayakumar
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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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Paul Dorbec, Seethu Varghese, Ambat Vijayakumar. 2016-03-23. Heredity for generalized power domination. https://arxiv.org/abs/1603.07243

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