Generalized power domination of graphs

  • Authors:

  • Gerard Jennhwa Chang;Paul Dorbec;Mickael Montassier;André Raspaud

  • Affiliations:

  • Department of Mathematics and Taida Institute for Mathematical Sciences, National Taiwan University, Taipei 10617, Taiwan and National Center for Theoretical Sciences, Taipei Office, Taiwan;Université de Bordeaux-CNRS, LaBRI, 351 cours de la Libération, 33405 Talence Cedex, France;Université de Bordeaux-CNRS, LaBRI, 351 cours de la Libération, 33405 Talence Cedex, France;Université de Bordeaux-CNRS, LaBRI, 351 cours de la Libération, 33405 Talence Cedex, France

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2012

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Abstract

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 and for bipartite graphs. We then give a linear algorithm for the problem on trees. Finally, we propose sharp upper bounds for the power domination number of connected graphs and of connected claw-free (k+2)-regular graphs.