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arXiv · 2209.14906

Quantum isomorphic strongly regular graphs from the $E_8$ root system

Simon Schmidt
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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 $120$ lines spanned by the $E_8$ root system and a rank $4$ graph whose complement was first discovered by Brouwer, Ivanov and Klin. Both graphs are strongly regular with parameters $(120, 63, 30, 36)$. Using Godsil-McKay switching, we obtain more quantum isomorphic, non-isomorphic strongly regular graphs with the same parameters.

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Simon Schmidt. 2022-09-29. Quantum isomorphic strongly regular graphs from the $E_8$ root system. https://arxiv.org/abs/2209.14906

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