Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

7-17-2020

Journal or Book Title

arXiv

Abstract

If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries ±1, 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 Kn, Kn/2,n/2, 2Kn/2, and nK1, 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.

Comments

This preprint is made available through arXiv: https://arxiv.org/abs/2007.09235.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

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