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

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

Econometrics and OR

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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
Publication status	Published - 2008

Keywords

minimum rank
rank
graph
symmetric matrix
matrix

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Barioli, F., Barrett, W., Butler, S., Cioabǎ, S. M., Cvetković, D., Fallat, S. M., Godsil, C. D., Haemers, W. H., Hogben, L., Mikkelson, R., Narayan, S. K., Pryporova, O., Sciriha, I., So, W., Stevanovic, D., van der Holst, H., Vander Meulen, K., & Wangsness Wehe, A. (2008). Zero forcing sets and minimum rank of graphs. Linear Algebra and its Applications, 428(7), 1628-1648.

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T1 - Zero forcing sets and minimum rank of graphs

AU - Barioli, Francesco

AU - Barrett, Wayne

AU - Butler, Steve

AU - Cioabǎ, S.M.

AU - Cvetković, D.

AU - Fallat, Shaun M.

AU - Godsil, Chris D.

AU - Haemers, W.H.

AU - Hogben, Leslie

AU - Mikkelson, Rana

AU - Narayan, Sivaram K.

AU - Pryporova, Olga

AU - Sciriha, Irene

AU - So, Wasin

AU - Stevanovic, Dragan

AU - van der Holst, Hein

AU - Vander Meulen, Kevin

AU - Wangsness Wehe, Amy

PY - 2008

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AB - The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric realmatrices whose ijth entry (for i /= j ) is nonzero whenever {i, j } is an edge in G and is zero otherwise. Thispaper introduces a new graph parameter, Z(G), that is the minimum size of a zero forcing set of verticesand uses it to bound the minimum rank for numerous families of graphs, often enabling computation of theminimum rank.

KW - minimum rank

KW - rank

KW - graph

KW - symmetric matrix

KW - matrix

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 minimum rank of graphs

Abstract

Keywords

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