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Article Dans Une Revue Acta Applicandae Mathematicae Année : 2014

Generalized power domination: propagation radius and Sierpinski Graphs

Paul Dorbec

Résumé

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 v are not yet in X, we get X=V(G). In this paper the k-power domination number of Sierpiński graphs is determined. The propagation radius is introduced as a measure of the efficiency of power dominating sets. The propagation radius of Sierpiński graphs is obtained in most of the cases.
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Dates et versions

hal-00975971 , version 1 (11-04-2024)

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Paul Dorbec, Sandi Klavzar. Generalized power domination: propagation radius and Sierpinski Graphs. Acta Applicandae Mathematicae, 2014, pp.DOI 10.1007/s10440-014-9870-7. ⟨10.1007/s10440-014-9870-7⟩. ⟨hal-00975971⟩

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