Journal of Combinatorial Optimization

, Volume 34, Issue 3, pp 736–741 | Cite as

Note on power propagation time and lower bounds for the power domination number

  • Daniela Ferrero
  • Leslie HogbenEmail author
  • Franklin H. J. Kenter
  • Michael Young


We present a counterexample to a lower bound for the power domination number given in Liao (J Comb Optim 31:725–742, 2016). We also define the power propagation time, using the power domination propagation ideas in Liao and the (zero forcing) propagation time in Hogben et al. (Discrete Appl Math 160:1994–2005, 2012).


Power domination Power propagation time Propagation time Time constraint 

Mathematics Subject Classification

05C69 05C12 05C15 05C57 94C15 


  1. Aazami A (2010) Domination in graphs with bounded propagation: algorithms, formulations and hardness results. J Comb Optim 19:429–456MathSciNetCrossRefzbMATHGoogle Scholar
  2. Aazami A (2008) Hardness results and approximation algorithms for some problems on graphs. PhD Thesis, University of Waterloo.
  3. AIM Minimum Rank – Special Graphs Work Group, Barioli F, Barrett W, Butler S, Cioaba SM, Cvetković D, Fallat SM, Godsil C, Haemers W, Hogben L, Mikkelson R, Narayan S, Pryporova O, Sciriha I, So W, Stevanović D, van der Holst H, Vander Meulen K, Wehe AW (2008) Zero forcing sets and the minimum rank of graphs. Linear Algebra Appl 428:1628–1648Google Scholar
  4. Baldwin TL, Mili L, Boisen MB Jr, Adapa R (1993) Power system observability with minimal phasor measurement placement. IEEE Trans Power Syst 8:707–715CrossRefGoogle Scholar
  5. Benson KF, Ferrero D, Flagg M, Furst V, Hogben L, Vasilevska V, Wissman B Power domination and zero forcing. Under review. arxiv:1510.02421
  6. Brueni DJ, Heath LS (2005) The PMU placement problem. SIAM J Discrete Math 19:744–761MathSciNetCrossRefzbMATHGoogle Scholar
  7. Burgarth D, Giovannetti V (2007) Full control by locally induced relaxation. Phys Rev Lett PRL 99:100501CrossRefGoogle Scholar
  8. Guo J, Niedermeier R, Raible D (2008) Improved algorithms and complexity results for power domination in graphs. Algorithmica 52:177–202MathSciNetCrossRefzbMATHGoogle Scholar
  9. Haynes TW, Hedetniemi SM, Hedetniemi ST, Henning MA (2002) Domination in graphs applied to electric power networks. SIAM J Discrete Math 15:519–529MathSciNetCrossRefzbMATHGoogle Scholar
  10. Hogben L, Huynh M, Kingsley N, Meyer S, Walker S, Young M (2012) Propagation time for zero forcing on a graph. Discrete Appl Math 160:1994–2005MathSciNetCrossRefzbMATHGoogle Scholar
  11. Liao C-S (2016) Power domination with bounded time constraints. J Comb Optim 31:725–742MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsTexas State UniversitySan MarcosUSA
  2. 2.Department of MathematicsIowa State UniversityAmesUSA
  3. 3.American Institute of MathematicsSan JoseUSA
  4. 4.Department of Computational and Applied MathematicsRice UniversityHoustonUSA

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