The maximum nullity of a complete edge subdivision graph is equal to it zero forcing number
| dc.contributor.author | Barrett, Wayne | |
| dc.contributor.author | Butler, Steve | |
| dc.contributor.author | Catral, Minnie | |
| dc.contributor.author | Hall, Tracy | |
| dc.contributor.author | Fallat, Shaun | |
| dc.contributor.author | Hogben, Leslie | |
| dc.contributor.author | Young, Michael | |
| dc.date.accessioned | 2015-05-12T16:31:28Z | |
| dc.date.available | 2015-05-12T16:31:28Z | |
| dc.date.issued | 2014-06 | |
| dc.description.abstract | Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all complete subdivision graphs. We prove that this equality holds. Furthermore, we compute the value of M(F, °G) = Z(°G) by introducing the bridge tree of a connected graph. Since this equality is valid for all fields, °G has field independent minimum rank, and we also show that °G has a universally optimal matrix. | en_US |
| dc.description.authorstatus | Faculty | en_US |
| dc.description.peerreview | yes | en_US |
| dc.description.sponsorship | NSERC | en_US |
| dc.identifier.uri | https://hdl.handle.net/10294/5682 | |
| dc.language.iso | en | en_US |
| dc.publisher | International Linear Algebra Society | en_US |
| dc.subject | zero forcing number | en_US |
| dc.title | The maximum nullity of a complete edge subdivision graph is equal to it zero forcing number | en_US |
| dc.type | Article | en_US |