Corpus ID: 220647001

Hadamard diagonalizable graphs of order at most 36

@article{Breen2020HadamardDG,
title={Hadamard diagonalizable graphs of order at most 36},
author={Jane Breen and S. Butler and Melissa Fuentes and Bernard Lidick'y and Michael Phillips and Alexander W. N. Riasanovksy and Sung Y. Song and R. R. Villagr{\'a}n and Cedar Wiseman and Xiaohong Zhang},
journal={arXiv: Combinatorics},
year={2020}
}
If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries $\pm1$, then the matrix formed by taking the columns as the eigenvectors is a Hadamard matrix and the graph is said to be Hadamard diagonalizable. In this article, we prove that if $n=8k+4$ the only possible Hadamard diagonalizable graphs are $K_n$, $K_{n/2,n/2}$, $2K_{n/2}$, and $nK_1$, and we develop an efficient computation for determining all graphs diagonalized by a given Hadamard matrix of any order… Expand

References

SHOWING 1-10 OF 10 REFERENCES
Perfect quantum state transfer using Hadamard diagonalizable graphs
• Mathematics, Physics
• 2017
Abstract Quantum state transfer within a quantum computer can be achieved by using a network of qubits, and such a network can be modelled mathematically by a graph. Here, we focus on theExpand
Perfect state transfer in products and covers of graphs
• Mathematics, Physics
• 2015
A continuous-time quantum walk on a graph is represented by the complex matrix , where is the adjacency matrix of and is a non-negative time. If the graph models a network of interacting qubits,Expand
On Hadamard diagonalizable graphs
• Mathematics
• 2011
Of interest here is a characterization of the undirected graphs G such that the Laplacian matrix associated with G can be diagonalized by some Hadamard matrix. Many interesting and fundamentalExpand
On construction and identification of graphs
Some remarks about the problem of graph identification.- Motivation.- A construction of a stationary graph.- Properties of cells.- Properties of cellular algebras of rank greater than one.- CellularExpand
Balancedly splittable Hadamard matrices
• Mathematics, Computer Science
• Discret. Math.
• 2019
A connection is made to the Hadamard diagonalizable strongly regular graphs, maximal equiangular lines set, and unbiased hadamard matrices. Expand
Basics of perfect communication through quantum networks
• A. Kay
• Mathematics, Physics
• 2011
Perfect transfer of a quantum state through a one-dimensional chain is now well understood, allowing one not only to decide whether a fixed Hamiltonian achieves perfect transfer but to design aExpand
Practical graph isomorphism, II
• Computer Science, Mathematics
• J. Symb. Comput.
• 2014
The description of the best known program nauty is brought up to date and an innovative approach called Traces that outperforms the competitors for many difficult graph classes is described. Expand
Complex Hadamard diagonalisable graphs
• Mathematics, Physics
• 2020
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.Expand
GNU Parallel: The Command-Line Power Tool
• Ole Tange
• Computer Science
• login Usenix Mag.
• 2011
Complex Hadamard diagonalizable graphs, arXiv:2001.00251v1 [math.CO
• 2001