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Minimum rank and zero forcing number for butterfly networks

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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.

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Notes

  1. OEIS:A001045

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Acknowledgements

We would like to thank an anonymous reviewer for carefully reading a previous version of the paper and providing a large number of insightful comments which were incredibly helpful in clarifying the presentation of our arguments.

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Authors and Affiliations

  1. Department of Mathematics, Texas State University, San Marcos, USA

    Daniela Ferrero

  2. School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, Australia

    Cyriac Grigorious, Thomas Kalinowski, Joe Ryan & Sudeep Stephen

  3. Graduate School, Kings College London, London, UK

    Cyriac Grigorious

  4. School of Science and Technology, University of New England, Armidale, Australia

    Thomas Kalinowski

  5. School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, India

    Sudeep Stephen

Authors
  1. Daniela Ferrero
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  2. Cyriac Grigorious
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  3. Thomas Kalinowski
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  4. Joe Ryan
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  5. Sudeep Stephen
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Correspondence to Thomas Kalinowski.

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Ferrero, D., Grigorious, C., Kalinowski, T. et al. Minimum rank and zero forcing number for butterfly networks. J Comb Optim 37, 970–988 (2019). https://doi.org/10.1007/s10878-018-0335-1

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  • DOI: https://doi.org/10.1007/s10878-018-0335-1

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