Heredity for generalized power domination

Paul Dorbec (1) , Seethu Varghese (2) , Ambat Vijayakumar (2)

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

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.

Mots clés: power domination; heredity; vertex deletion; edge deletion; edge contraction; propagation radius

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Paul Dorbec, Seethu Varghese, Ambat Vijayakumar. Heredity for generalized power domination. 2015. ⟨hal-01207482v1⟩