### Abstract

Original language | English |
---|---|

Pages (from-to) | 1628-1648 |

Journal | Linear Algebra and Its Applications |

Volume | 428 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2008 |

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### Cite this

*Linear Algebra and Its Applications*,

*428*(7), 1628-1648. https://doi.org/10.1016/j.laa.2007.10.009

}

*Linear Algebra and Its Applications*, vol. 428, no. 7, pp. 1628-1648. https://doi.org/10.1016/j.laa.2007.10.009

**Zero forcing sets and the minimum rank of graphs.** / Holst, van der, H.; Barioli, F.; Barrett, W.; Butler, S.; Cioaba, S.M.; Cvetkovic, D.M.; Fallat, S.M.; Godsil, C.D.; Haemers, W.H.; Hogben, L.; Mikkelson, R.; Narayan, S.; Pryporova, O.; Sciriha, I.; So, W.; Stevanovic, D.; Vander Meulen, K.N.; Wangsness Wehe, A.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Zero forcing sets and the minimum rank of graphs

AU - Holst, van der, H.

AU - Barioli, F.

AU - Barrett, W.

AU - Butler, S.

AU - Cioaba, S.M.

AU - Cvetkovic, D.M.

AU - Fallat, S.M.

AU - Godsil, C.D.

AU - Haemers, W.H.

AU - Hogben, L.

AU - Mikkelson, R.

AU - Narayan, S.

AU - Pryporova, O.

AU - Sciriha, I.

AU - So, W.

AU - Stevanovic, D.

AU - Vander Meulen, K.N.

AU - Wangsness Wehe, A.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

U2 - 10.1016/j.laa.2007.10.009

DO - 10.1016/j.laa.2007.10.009

M3 - Article

VL - 428

SP - 1628

EP - 1648

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 7

ER -