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Article
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
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
4-1-2008
DOI
10.1016/j.laa.2007.10.009
Abstract

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.

Comments

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.

Rights
This manuscript version is made available under the CCBY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright Owner
Elsevier Inc.
Language
en
File Format
application/pdf
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)
Available at: http://0-works.bepress.com.library.simmons.edu/leslie-hogben/79/