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

Author

Listed:
  • Daniela Ferrero

    (Texas State University)

  • Leslie Hogben

    (Iowa State University
    American Institute of Mathematics)

  • Franklin H. J. Kenter

    (Rice University)

  • Michael Young

    (Iowa State University)

Abstract

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).

Suggested Citation

  • Daniela Ferrero & Leslie Hogben & Franklin H. J. Kenter & Michael Young, 2017. "Note on power propagation time and lower bounds for the power domination number," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 736-741, October.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:3:d:10.1007_s10878-016-0103-z
    DOI: 10.1007/s10878-016-0103-z
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    References listed on IDEAS

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    1. Ashkan Aazami, 2010. "Domination in graphs with bounded propagation: algorithms, formulations and hardness results," Journal of Combinatorial Optimization, Springer, vol. 19(4), pages 429-456, May.
    2. Chung-Shou Liao, 2016. "Power domination with bounded time constraints," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 725-742, February.
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    Cited by:

    1. Chassidy Bozeman & Boris Brimkov & Craig Erickson & Daniela Ferrero & Mary Flagg & Leslie Hogben, 2019. "Restricted power domination and zero forcing problems," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 935-956, April.
    2. Boris Brimkov & Derek Mikesell & Logan Smith, 2019. "Connected power domination in graphs," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 292-315, July.

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