Zero forcing sets and minimum rank of graphs

Francesco Barioli, Wayne Barrett, Steve Butler, S.M. Cioabǎ, D. Cvetković, Shaun M. Fallat, Chris D. Godsil, W.H. Haemers, Leslie Hogben, Rana Mikkelson, Sivaram K. Narayan, Olga Pryporova, Irene Sciriha, Wasin So, Dragan Stevanovic, Hein van der Holst, Kevin Vander Meulen, Amy Wangsness Wehe

Research output: Contribution to journalArticleScientificpeer-review

291 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)1628-1648
JournalLinear Algebra and its Applications
Issue number7
Publication statusPublished - 2008


  • minimum rank
  • rank
  • graph
  • symmetric matrix
  • matrix


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