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Minimum rank and zero forcing number for butterfly networks

  • Daniela Ferrero
  • Cyriac Grigorious
  • Thomas Kalinowski
  • Joe Ryan
  • Sudeep Stephen
Article
  • 43 Downloads

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.

Keywords

Zero forcing Minimum rank of graphs Butterfly network 

Mathematics Subject Classification

05C96 05C57 94C15 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTexas State UniversitySan MarcosUSA
  2. 2.School of Mathematical and Physical SciencesUniversity of NewcastleCallaghanAustralia
  3. 3.Graduate SchoolKings College LondonLondonUK
  4. 4.School of Science and TechnologyUniversity of New EnglandArmidaleAustralia
  5. 5.School of Mathematical SciencesNational Institute of Science Education and ResearchBhubaneswarIndia

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