Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph Edholm, Christina Hogben, Leslie Hogben, Leslie Huynh, My LaGrange, Josh Row, Darren
dc.contributor.department Mathematics 2019-06-28T22:11:38.000 2020-06-30T06:00:26Z 2020-06-30T06:00:26Z Fri Jan 01 00:00:00 UTC 2010 2012-06-15
dc.description.abstract <p>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 not equal j) is nonzero whenever {i, j} is an edge in G and is zero otherwise; maximum nullity is taken over the same set of matrices. The zero forcing number is the minimum size of a zero forcing set of vertices and bounds the maximum nullity from above. The spread of a graph parameter at a vertex v or edge e of G is the difference between the value of the parameter on G and on G - v or G - e. Rank spread (at a vertex) was introduced in [4]. This paper introduces vertex spread of the zero forcing number and edge spreads for minimum rank/maximum nullity and zero forcing number. Properties of the spreads are established and used to determine values of the minimum rank/maximum nullity and zero forcing number for various types of grids with a vertex or edge deleted.</p>
dc.description.comments <p>This is a manuscript of an article published as Edholm, Christina J., Leslie Hogben, My Huynh, Joshua LaGrange, and Darren D. Row. "Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph." <em>Linear Algebra and its Applications</em> 436, no. 12 (2012): 4352-4372. DOI: <a href="" target="_blank">10.1016/j.laa.2010.10.015</a>. Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/
dc.identifier.articleid 1217
dc.identifier.contextkey 14438203
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/211
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 22:34:49 UTC 2022
dc.source.uri 10.1016/j.laa.2010.10.015
dc.subject.disciplines Discrete Mathematics and Combinatorics
dc.subject.keywords zero spread
dc.subject.keywords null spread
dc.subject.keywords rank spread
dc.subject.keywords zero forcing number
dc.subject.keywords maximum nullity
dc.subject.keywords minimum rank
dc.subject.keywords supertriangle
dc.subject.keywords grid graph
dc.subject.keywords triangular grid
dc.subject.keywords king grid
dc.title Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph
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
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
860.08 KB
Adobe Portable Document Format