Generalized Power Domination: Propagation Radius and Sierpiński Graphs
نویسندگان
چکیده
منابع مشابه
Generalized power domination: propagation radius and Sierpiński graphs
The recently introduced concept of k-power domination generalizes domination and power domination, the latter concept being used for monitoring an electric power system. The k-power domination problem is to determine a minimum size vertex subset S of a graph G such that after setting X = N [S], and iteratively adding to X vertices x that have a neighbour v in X such that at most k neighbours of...
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In this paper, we introduce the concept of k-power domination which is a common generalization of domination and power domination. We extend several known results for power domination to k-power domination. Concerning the complexity of the k-power domination problem, we first show that deciding whether a graph admits a k-power dominating set of size at most t is NP-complete for chordal graphs a...
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The power dominating problem is a variation of the classical domination problem in graphs. Electricity company use phase measurement units (PMUs) to produce the measuring data of a system, and use these data to estimate states of the system. Because of the high cost of PMUs, minimizing the number of PMUs on a system is an important problem for electricity companies. This problem can be modeled ...
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In this paper, we continue the study of power domination in graphs (see SIAM J. Discrete Math. 15 (2002), 519–529; SIAM J. Discrete Math. 22 (2008), 554–567; SIAM J. Discrete Math. 23 (2009), 1382–1399). Power domination in graphs was birthed from the problem of monitoring an electric power system by placing as few measurement devices in the system as possible. A set of vertices is defined to b...
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A set S of vertices is defined to be a power dominating set (PDS) of a graph G if every vertex and every edge in G can be monitored by the set S according to a set of rules for power system monitoring. The minimum cardinality of a PDS of G is its power domination number. In this article, we find upper bounds for the power domination number of some families of Cartesian products of graphs: the c...
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ژورنال
عنوان ژورنال: Acta Applicandae Mathematicae
سال: 2014
ISSN: 0167-8019,1572-9036
DOI: 10.1007/s10440-014-9870-7