Quantum isomorphic strongly regular graphs from the E 8 root system
Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 515-528.

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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DOI: 10.5802/alco.335
Classification: 05E30, 20B25, 05C25, 17B22, 20G42
Keywords: strongly regular graphs, quantum isomorphism, root systems, Godsil–McKay switching
Schmidt, Simon 1

1 QMATH Department of Mathematical Sciences University of Copenhagen Universitetsparken 5 2100 Copenhagen Ø Denmark
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Schmidt, Simon. Quantum isomorphic strongly regular graphs from the $E_8$ root system. Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 515-528. doi : 10.5802/alco.335. https://alco.centre-mersenne.org/articles/10.5802/alco.335/

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