Quantum isomorphic strongly regular graphs from the E8 root system
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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 E8 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.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Algebraic Combinatorics |
| Vol/bind | 7 |
| Udgave nummer | 2 |
| Sider (fra-til) | 515-528 |
| Antal sider | 14 |
| ISSN | 2589-5486 |
| DOI | |
| Status | Udgivet - 2024 |
Bibliografisk note
Funding Information:
The author has received funding from the European Union\u2019s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 101030346. He thanks David Roberson for helpful discussions on quantum isomorphisms and graph switching. He furthermore thanks the reviewer for valuable comments.
Funding Information:
Acknowledgements. The author has received funding from the European Union\u2019s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 101030346. He thanks David Roberson for helpful discussions on quantum isomorphisms and graph switching. He furthermore thanks the reviewer for valuable comments.
Publisher Copyright:
© The author(s), 2024.
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