Quantum isomorphic strongly regular graphs from the $E_8$ root system
Combinatorics
2022-09-30 v1 Quantum Algebra
Abstract
In this article, we give a first example of a pair of quantum isomorphic, non-isomorphic strongly regular graphs, that is, non-isomorphic strongly regular graphs having the same homomorphism counts from all planar graphs. The pair consists of the orthogonality graph of the lines spanned by the root system and a rank graph whose complement was first discovered by Brouwer, Ivanov and Klin. Both graphs are strongly regular with parameters . Using Godsil-McKay switching, we obtain more quantum isomorphic, non-isomorphic strongly regular graphs with the same parameters.
Keywords
Cite
@article{arxiv.2209.14906,
title = {Quantum isomorphic strongly regular graphs from the $E_8$ root system},
author = {Simon Schmidt},
journal= {arXiv preprint arXiv:2209.14906},
year = {2022}
}