Hadamard diagonalizable graphs of order at most 36

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dc.contributor.author Breen, Jane
dc.contributor.author Lidicky, Bernard
dc.contributor.author Butler, Steve
dc.contributor.author Fuentes, Melissa
dc.contributor.author Lidicky, Bernard
dc.contributor.author Phillips, Michael
dc.contributor.author Riasanovsky, Alexander
dc.contributor.author Song, Sung-Yell
dc.contributor.author Villagrán, Ralihe
dc.contributor.author Wiseman, Cedar
dc.contributor.author Zhang, Xiaohong
dc.contributor.department Mathematics
dc.date 2020-07-27T15:30:08.000
dc.date.accessioned 2021-02-26T02:54:13Z
dc.date.available 2021-02-26T02:54:13Z
dc.date.copyright Wed Jan 01 00:00:00 UTC 2020
dc.date.issued 2020-07-17
dc.description.abstract <p>If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries ±1, then the matrix formed by taking the columns as the eigenvectors is a Hadamard matrix and the graph is said to be Hadamard diagonalizable.<br />In this article, we prove that if n=8k+4 the only possible Hadamard diagonalizable graphs are Kn, Kn/2,n/2, 2Kn/2, and nK1, and we develop an efficient computation for determining all graphs diagonalized by a given Hadamard matrix of any order. Using these two tools, we determine and present all Hadamard diagonalizable graphs up to order 36. Note that it is not even known how many Hadamard matrices there are of order 36.</p>
dc.description.comments <p>This preprint is made available through arXiv: <a href="https://arxiv.org/abs/2007.09235">https://arxiv.org/abs/2007.09235</a>.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/math_pubs/239/
dc.identifier.articleid 1246
dc.identifier.contextkey 18666566
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/239
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/96634
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/math_pubs/239/2020_Lidicky_HadamardDiagonalizablePreprint.pdf|||Fri Jan 14 22:50:08 UTC 2022
dc.subject.disciplines Algebra
dc.subject.disciplines Discrete Mathematics and Combinatorics
dc.subject.keywords Hadamard matrix
dc.subject.keywords Laplacian matrix
dc.subject.keywords Cayley graph
dc.subject.keywords graph product
dc.subject.keywords experimental mathematics
dc.title Hadamard diagonalizable graphs of order at most 36
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication a1d8f5ab-9124-4104-981c-8ba1e426e3ff
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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