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Minimum rank and zero forcing number for butterfly networks

Author

Listed:
  • Daniela Ferrero

    (Texas State University)

  • Cyriac Grigorious

    (University of Newcastle
    Kings College London)

  • Thomas Kalinowski

    (University of Newcastle
    University of New England)

  • Joe Ryan

    (University of Newcastle)

  • Sudeep Stephen

    (University of Newcastle
    National Institute of Science Education and Research)

Abstract

Zero forcing is a graph propagation process introduced in quantum physics and theoretical computer science, and closely related to the minimum rank problem. The minimum rank of a graph is the smallest possible rank over all matrices described by a given network. We use this relationship to determine the minimum rank and the zero forcing number of butterfly networks, concluding they present optimal properties in regards to both problems.

Suggested Citation

  • Daniela Ferrero & Cyriac Grigorious & Thomas Kalinowski & Joe Ryan & Sudeep Stephen, 2019. "Minimum rank and zero forcing number for butterfly networks," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 970-988, April.
    • Handle: RePEc:spr:jcomop:v:37:y:2019:i:3:d:10.1007_s10878-018-0335-1
    DOI: 10.1007/s10878-018-0335-1
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    Cited by:

    1. Randy Davila & Michael A. Henning, 2021. "Zero forcing versus domination in cubic graphs," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 553-577, February.

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