Reconfiguration graphs of zero forcing sets

dc.contributor.author Geneson, Jesse
dc.contributor.author Haas, Ruth
dc.contributor.author Hogben, Leslie
dc.contributor.department Mathematics
dc.date 2021-07-07T22:18:25.000
dc.date.accessioned 2021-08-14T19:03:46Z
dc.date.available 2021-08-14T19:03:46Z
dc.date.copyright Wed Jan 01 00:00:00 UTC 2020
dc.date.issued 2020-01-01
dc.description.abstract <p>This paper begins the study of reconfiguration of zero forcing sets, and more specifically, the zero forcing graph. Given a base graph G, its zero forcing graph, Z(G), is the graph whose vertices are the minimum zero forcing sets of G with an edge between vertices B and B′ of Z(G) if and only if B can be obtained from B′ by changing a single vertex of G. It is shown that the zero forcing graph of a forest is connected, but that many zero forcing graphs are disconnected. We characterize the base graphs whose zero forcing graphs are either a path or the complete graph, and show that the star cannot be a zero forcing graph. We show that computing Z(G) takes 2Θ(n) operations in the worst case for a graph G of order n.</p>
dc.description.comments <p>This is a pre-print of the article Geneson, Jesse, Ruth Haas, and Leslie Hogben. "Reconfiguration graphs of zero forcing sets." <em>arXiv preprint arXiv:2009.00220</em> (2020). Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/math_pubs/273/
dc.identifier.articleid 1280
dc.identifier.contextkey 23712421
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/273
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/1wgeXdMr
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/math_pubs/273/2020_HogbenLeslie_ReconfigurationGraphs.pdf|||Fri Jan 14 23:07:00 UTC 2022
dc.subject.disciplines Discrete Mathematics and Combinatorics
dc.subject.keywords reconfiguration
dc.subject.keywords zero forcing
dc.subject.keywords zero forcing graph
dc.title Reconfiguration graphs of zero forcing sets
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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