Zero forcing and power domination for graph products

dc.contributor.author Benson, Katherine
dc.contributor.author Ferrero, Daniela
dc.contributor.author Flagg, Mary
dc.contributor.author Hogben, Leslie
dc.contributor.author Furst, Veronika
dc.contributor.author Hogben, Leslie
dc.contributor.author Vasilevska, Violeta
dc.contributor.author Wissman, Brian
dc.contributor.department Electrical and Computer Engineering
dc.contributor.department Mathematics
dc.date 2018-04-09T18:59:37.000
dc.date.accessioned 2020-06-30T06:00:05Z
dc.date.available 2020-06-30T06:00:05Z
dc.date.copyright Mon Jan 01 00:00:00 UTC 2018
dc.date.issued 2018-01-01
dc.description.abstract <p>The power domination number arose from the monitoring of electrical networks, and methods for its determination have the associated application. The zero forcing number arose in the study of maximum nullity among symmetric matrices described by a graph (and also in control of quantum systems and in graph search algorithms). There has been considerable effort devoted to the determination of the power domination number, the zero forcing number, and maximum nullity for specific families of graphs. In this paper we exploit the natural relationship between power domination and zero forcing to obtain results for the power domination number of tensor products and the zero forcing number of lexicographic products of graphs. In addition, we establish a general lower bound for the power domination number of a graph based on the maximum nullity of the matrices described by the graph. We also establish results for the zero forcing number and maximum nullity of tensor products and Cartesian products of certain graphs.</p>
dc.description.comments <p>This article is published as Benson, Katherine F., Daniela Ferrero, Mary Flagg, Veronika Furst, Leslie Hogben, Violeta Vasilevska, and Brian Wissman. "Zero forcing and power domination for graph products." <em>Australasian Journal of Combinatorics </em>70, no. 2 (2018): 221-235. https://ajc.maths.uq.edu.au/pdf/70/ajc_v70_p221.pdf</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/math_pubs/169/
dc.identifier.articleid 1177
dc.identifier.contextkey 11931016
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/169
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/54556
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/math_pubs/169/2018_Hogben_ZeroForcing.pdf|||Fri Jan 14 21:07:46 UTC 2022
dc.subject.disciplines Discrete Mathematics and Combinatorics
dc.subject.disciplines Mathematics
dc.subject.keywords Minimum rank
dc.subject.keywords Matrices
dc.subject.keywords Placement
dc.subject.keywords Sets
dc.title Zero forcing and power domination for graph products
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication 0131698a-00df-41ad-8919-35fb630b282b
relation.isOrgUnitOfPublication a75a044c-d11e-44cd-af4f-dab1d83339ff
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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