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Zero forcing sets and the minimum rank of graphs
Linear Algebra and its Applications
  • Francesco Barioli, University of Tennessee at Chattanooga
  • Wayne Barrett, Brigham Young University
  • Steve Butler, University of California, San Diego
  • Sebastian M. Cioabă, University of California, San Diego
  • Dragoš Cvetković, University of Belgrade
  • Shaun M. Fallat, University of Regina
  • Chris Godsil, University of Waterloo
  • Willem Haemers, Tilburg University
  • Leslie Hogben, Iowa State University
  • Rana Mikkelson, Iowa State University
  • Sivaram Narayan, Central Michigan University
  • Olga Pryporova, Iowa State University
  • Irene Sciriha, University of Malta
  • Wasin So, San Jose State University
  • Dragan Stevanović, University of Nis
  • Hein van der Holst, Eindhoven University of Technology
  • Kevin Vander Meulen, Redeemer University College
  • Amy Wangsness Wehe, Fitchburg State College
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Accepted Manuscript
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The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. This paper introduces a new graph parameter, Z(G), that is the minimum size of a zero forcing set of vertices and uses it to bound the minimum rank for numerous families of graphs, often enabling computation of the minimum rank.


This is a manuscript of an article from Linear Algebra and its Applications 428 (2008): 1628, doi:10.1016/j.laa.2007.10.009. Posted with permission.

This manuscript version is made available under the CCBY-NC-ND 4.0 license
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Elsevier Inc.
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Citation Information
Francesco Barioli, Wayne Barrett, Steve Butler, Sebastian M. Cioabă, et al.. "Zero forcing sets and the minimum rank of graphs" Linear Algebra and its Applications Vol. 428 (2008)
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