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Connected power domination in graphs

  • Boris BrimkovEmail author
  • Derek Mikesell
  • Logan Smith
Article
  • 7 Downloads

Abstract

The study of power domination in graphs arises from the problem of placing a minimum number of measurement devices in an electrical network while monitoring the entire network. A power dominating set of a graph is a set of vertices from which every vertex in the graph can be observed, following a set of rules for power system monitoring. In this paper, we study the problem of finding a minimum power dominating set which is connected; the cardinality of such a set is called the connected power domination number of the graph. We show that the connected power domination number of a graph is NP-hard to compute in general, but can be computed in linear time in cactus graphs and block graphs. We also give various structural results about connected power domination, including a cut vertex decomposition and a characterization of the effects of various vertex and edge operations on the connected power domination number. Finally, we present novel integer programming formulations for power domination, connected power domination, and power propagation time, and give computational results.

Keywords

Connected power domination Power domination Cactus graph NP-complete Integer program Zero forcing 

Mathematics Subject Classification

05C69 05C57 94C15 

Notes

Acknowledgements

This work is supported by the National Science Foundation, under Grants CMMI-1634550, CMMI-1404864, and DMS-1720225, and by the Rice University Academy of Fellows.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computational and Applied MathematicsRice UniversityHoustonUSA

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