Quantum isomorphic strongly regular graphs from the E8 root system
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
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
APA
Vancouver
Author
Bibtex
}
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