Complex Hadamard diagonalisable graphs

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dc.contributor.authorChan, A.
dc.contributor.authorFallat, S.
dc.contributor.authorKirkland, S.
dc.contributor.authorLin, J.
dc.contributor.authorNasserasr, S.
dc.contributor.authorPlosker, S.
dc.date.accessioned2020-07-31T16:02:21Z
dc.date.available2020-07-31T16:02:21Z
dc.date.issued2020
dc.date.submitted2020-07-31T01:43:35Zen_US
dc.description.abstractIn light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex Hadamard matrices.We give some basic properties and methods of constructing such graphs. We show that a large class of complex Hadamard diagonalisable graphs have vertex sets forming an equitable partition, and that the Laplacian eigenvalues must be even integers. We provide a number of examples and constructions of complex Hadamard diagonalisable graphs, including two special classes of graphs: the Cayley graphs over Z^d_r , and the non–complete extended p–sum (NEPS). We discuss necessary and sufficient conditions for (\alpha, \beta)–Laplacian fractional revival and perfect state transfer on continuous–time quantum walks described by complex Hadamard diagonalisable graphs and provide examples of such quantum state transfer.en_US
dc.description.sponsorshipNSERC Discovery Grant number RGPIN–2019–05408.en_US
dc.identifier.urihttp://hdl.handle.net/1993/34815
dc.language.isoengen_US
dc.publisherLinear Algebra and its Applicationsen_US
dc.rightsrestricted accessen_US
dc.statusyes
dc.subjectcomplex Hadamard matrixen_US
dc.subjecttype II matrixen_US
dc.subjectCheeger inequalityen_US
dc.subjectequitable partitionen_US
dc.subjectquantum state transferen_US
dc.subjectgraph productsen_US
dc.titleComplex Hadamard diagonalisable graphsen_US
dc.typeArticleen_US
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