Hadamard diagonalizable graphs of order at most 36
Combinatorics
2020-08-18 v2
Abstract
If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries , 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 the only possible Hadamard diagonalizable graphs are , , , and , 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.
Keywords
Cite
@article{arxiv.2007.09235,
title = {Hadamard diagonalizable graphs of order at most 36},
author = {Jane Breen and Steve Butler and Melissa Fuentes and Bernard Lidický and Michael Phillips and Alexander W. N. Riasanovksy and Sung-Yell Song and Ralihe R. Villagrán and Cedar Wiseman and Xiaohong Zhang},
journal= {arXiv preprint arXiv:2007.09235},
year = {2020}
}