The k-power bondage number of a graph
Seethu Varghese, A. Vijayakumar · Discrete Mathematics Algorithms and Applications · 2016
The [Formula: see text]-power domination number, [Formula: see text], of a graph [Formula: see text] is the minimum cardinality of a [Formula: see text]-power dominating set of [Formula: see text]. In this paper, we initiate the study of the [Formula: see text]-power bondage number, [Formula: see text], of a graph [Formula: see text], i.e., the minimum cardinality among all sets [Formula: see text] for which [Formula: see text]. We obtain a sharp upper bound for [Formula: see text] in terms of the degree of [Formula: see text]. We prove that [Formula: see text] for any nonempty tree [Formula: see text] and also provide some conditions on [Formula: see text] for [Formula: see text].