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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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.
In: Linear Algebra and Its Applications, Vol. 428, No. 7, 2008, p. 1628-1648.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 -