Quantum isomorphic strongly regular graphs from the E8 root system
Publikation: Working paper › Preprint › Forskning
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Quantum isomorphic strongly regular graphs from the E8 root system. / Schmidt, Simon.
arXiv preprint, 2022.Publikation: Working paper › Preprint › Forskning
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TY - UNPB
T1 - Quantum isomorphic strongly regular graphs from the E8 root system
AU - Schmidt, Simon
PY - 2022
Y1 - 2022
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.
UR - https://arxiv.org/abs/2209.14906
M3 - Preprint
BT - Quantum isomorphic strongly regular graphs from the E8 root system
PB - arXiv preprint
ER -
ID: 320873820