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\(k\)-Power domination in block graphs

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Abstract

The power system monitoring problem asks for as few as possible measurement devices to be put in an electric power system. The problem has a graph theory model involving power dominating set in graphs. The concept of \(k\)-power domination, first introduced by Chang et al. (Discret Appl Math 160:1691–1698, 2012), is a common generalization of domination and power domination. In this paper, we present a linear-time algorithm for \(k\)-power domination in block graphs.

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Acknowledgments

Supported in part by National Natural Science Foundation of China (Nos. 61202021, 11371008, 91230201, 61373028), Shanghai Educational Development Foundation (No. 12CG55), Innovation Program of Shanghai Municipal Education Commission (No. 12YZ120), Science & Technology Program of Shanghai Maritime University (20120105).

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200062, China

    Chao Wang & Changhong Lu

  2. College of Information Engineering, Shanghai Maritime University, Shanghai, 201306, China

    Lei Chen

Authors
  1. Chao Wang
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  2. Lei Chen
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  3. Changhong Lu
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Correspondence to Changhong Lu.

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Wang, C., Chen, L. & Lu, C. \(k\)-Power domination in block graphs. J Comb Optim 31, 865–873 (2016). https://doi.org/10.1007/s10878-014-9795-0

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  • DOI: https://doi.org/10.1007/s10878-014-9795-0

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