Quantum isomorphic strongly regular graphs from the E8 root system

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Quantum isomorphic strongly regular graphs from the E8 root system. / Schmidt, Simon.

In: Algebraic Combinatorics, Vol. 7, No. 2, 2024, p. 515-528.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Schmidt, S 2024, 'Quantum isomorphic strongly regular graphs from the E8 root system', Algebraic Combinatorics, vol. 7, no. 2, pp. 515-528. https://doi.org/10.5802/alco.335

APA

Schmidt, S. (2024). Quantum isomorphic strongly regular graphs from the E8 root system. Algebraic Combinatorics, 7(2), 515-528. https://doi.org/10.5802/alco.335

Vancouver

Schmidt S. Quantum isomorphic strongly regular graphs from the E8 root system. Algebraic Combinatorics. 2024;7(2):515-528. https://doi.org/10.5802/alco.335

Author

Schmidt, Simon. / Quantum isomorphic strongly regular graphs from the E8 root system. In: Algebraic Combinatorics. 2024 ; Vol. 7, No. 2. pp. 515-528.

Bibtex

@article{2806b694a0ec46cbb72f13f5dd74a944,
title = "Quantum isomorphic strongly regular graphs from the E8 root system",
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 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.",
keywords = "Godsil–McKay switching, quantum isomorphism, root systems, strongly regular graphs",
author = "Simon Schmidt",
note = "Publisher Copyright: {\textcopyright} The author(s), 2024.",
year = "2024",
doi = "10.5802/alco.335",
language = "English",
volume = "7",
pages = "515--528",
journal = "Algebraic Combinatorics",
issn = "2589-5486",
publisher = "Centre Mersenne",
number = "2",

}

RIS

TY - JOUR

T1 - Quantum isomorphic strongly regular graphs from the E8 root system

AU - Schmidt, Simon

N1 - Publisher Copyright: © The author(s), 2024.

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - Godsil–McKay switching

KW - quantum isomorphism

KW - root systems

KW - strongly regular graphs

U2 - 10.5802/alco.335

DO - 10.5802/alco.335

M3 - Journal article

AN - SCOPUS:85192394625

VL - 7

SP - 515

EP - 528

JO - Algebraic Combinatorics

JF - Algebraic Combinatorics

SN - 2589-5486

IS - 2

ER -

ID: 392562112