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Complex Hadamard diagonalisable graphs.
- Source :
-
Linear Algebra & its Applications . Nov2020, Vol. 605, p158-179. 22p. - Publication Year :
- 2020
-
Abstract
- In 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 r d , and the non–complete extended p –sum (NEPS). We discuss necessary and sufficient conditions for (α , β) –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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 605
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 145319720
- Full Text :
- https://doi.org/10.1016/j.laa.2020.07.018