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

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