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.
Copyright Owner
The Authors
Copyright Date
2020
Language
en
File Format
application/pdf
Recommended Citation
Breen, Jane; Butler, Steve; Fuentes, Melissa; Lidicky, Bernard; Phillips, Michael; Riasanovsky, Alexander W. N.; Song, Sung-Yell; Villagrán, Ralihe R.; Wiseman, Cedar; and Zhang, Xiaohong, "Hadamard diagonalizable graphs of order at most 36" (2020). Mathematics Publications. 239.
https://lib.dr.iastate.edu/math_pubs/239
Comments
This preprint is made available through arXiv: https://arxiv.org/abs/2007.09235.