Corpus ID: 220647001

Hadamard diagonalizable graphs of order at most 36

  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},
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

Figures and Tables from this paper


Perfect quantum state transfer using Hadamard diagonalizable graphs
On Hadamard diagonalizable graphs
Balancedly splittable Hadamard matrices
Basics of perfect communication through quantum networks
  • A. Kay
  • Mathematics, Physics
  • 2011
Practical graph isomorphism, II
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