Zero forcing sets and the minimum rank of graphs

H. Holst, van der; F. Barioli; W. Barrett; S. Butler; S.M. Cioaba; D.M. Cvetkovic; S.M. Fallat; C.D. Godsil; W.H. Haemers; L. Hogben; R. Mikkelson; S. Narayan; O. Pryporova; I. Sciriha; W. So; D. Stevanovic; K.N. Vander Meulen; A. Wangsness Wehe

doi:10.1016/j.laa.2007.10.009

Zero forcing sets and the minimum rank of graphs

H. Holst, van der, F. Barioli, W. Barrett, S. Butler, S.M. Cioaba, D.M. Cvetkovic, S.M. Fallat, C.D. Godsil, W.H. Haemers, L. Hogben, R. Mikkelson, S. Narayan, O. Pryporova, I. Sciriha, W. So, D. Stevanovic, K.N. Vander Meulen, A. Wangsness Wehe

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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.

Original language	English
Pages (from-to)	1628-1648
Journal	Linear Algebra and Its Applications
Volume	428
Issue number	7
DOIs	https://doi.org/10.1016/j.laa.2007.10.009
Publication status	Published - 2008

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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. (2008). Zero forcing sets and the minimum rank of graphs. Linear Algebra and Its Applications, 428(7), 1628-1648. https://doi.org/10.1016/j.laa.2007.10.009

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author = "{Holst, van der}, H. and F. Barioli and W. Barrett and S. Butler and S.M. Cioaba and D.M. Cvetkovic and S.M. Fallat and C.D. Godsil and W.H. Haemers and L. Hogben and R. Mikkelson and S. Narayan and O. Pryporova and I. Sciriha and W. So and D. Stevanovic and {Vander Meulen}, K.N. and {Wangsness Wehe}, A.",

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Holst, van der, H, Barioli, F, Barrett, W, Butler, S, Cioaba, SM, Cvetkovic, DM, Fallat, SM, Godsil, CD, Haemers, WH, Hogben, L, Mikkelson, R, Narayan, S, Pryporova, O, Sciriha, I, So, W, Stevanovic, D, Vander Meulen, KN & Wangsness Wehe, A 2008, 'Zero forcing sets and the minimum rank of graphs', Linear Algebra and Its Applications, vol. 428, no. 7, pp. 1628-1648. https://doi.org/10.1016/j.laa.2007.10.009

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

SN - 0024-3795

VL - 428

SP - 1628

EP - 1648

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 7

ER -

Zero forcing sets and the minimum rank of graphs

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