Orthogonal representations, minimum rank, and graph complements

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dc.contributor.author Hogben, Leslie
dc.contributor.author Hogben, Leslie
dc.contributor.department Mathematics
dc.date 2018-02-18T06:08:09.000
dc.date.accessioned 2020-06-30T06:01:00Z
dc.date.available 2020-06-30T06:01:00Z
dc.date.copyright Mon Jan 01 00:00:00 UTC 2007
dc.date.issued 2008-06-01
dc.description.abstract <p>Orthogonal representations are used to show that complements of certain sparse graphs have (positive semidefinite) minimum rank at most 4. This bound applies to the complement of a 2-tree and to the complement of a unicyclic graph. Hence for such graphs, the sum of the minimum rank of the graph and the minimum rank of its complement is at most two more than the order of the graph. The minimum rank of the complement of a 2-tree is determined exactly.</p>
dc.description.comments <p>This is a manuscript of an article from <em>Linear Algebra and its Applications </em>428 (2008); 2560, doi:<a href="http://dx.doi.org/10.1016/j.laa.2007.12.004" target="_blank">10.1016/j.laa.2007.12.004</a>. Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/math_pubs/87/
dc.identifier.articleid 1080
dc.identifier.contextkey 9889926
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/87
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/54686
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/math_pubs/87/2008_Hogben_OrthogonalRepresentations.pdf|||Sat Jan 15 02:15:34 UTC 2022
dc.source.uri 10.1016/j.laa.2007.12.004
dc.subject.disciplines Algebra
dc.subject.disciplines Discrete Mathematics and Combinatorics
dc.subject.keywords Minimum rank
dc.subject.keywords Orthogonal representation
dc.subject.keywords 2-Tree
dc.subject.keywords Unicyclic graph
dc.subject.keywords Graph complement
dc.title Orthogonal representations, minimum rank, and graph complements
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication 0131698a-00df-41ad-8919-35fb630b282b
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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