Quantum automorphisms of folded cube graphs  [ Automorphismes quantiques des graphes des cubes pliés ]
Annales de l'Institut Fourier, Tome 70 (2020) no. 3, pp. 949-970.

On démontre que le groupe quantique d’automorphismes du graphe de Clebsch est SO 5 -1 ce qui répond à une question de Banica, Bichon et Collins de 2007. En général, pour des valeurs impaires de n, le groupe quantique d’automorphisme du graphe du n-cube plié est SO n -1 . En plus, on démontre qu’un graphe possède des symétries quantiques, si son groupe d’automorphismes contient une paire d’automorphismes disjoints.

We show that the quantum automorphism group of the Clebsch graph is SO 5 -1 . This answers a question by Banica, Bichon and Collins from 2007. More general for odd n, the quantum automorphism group of the folded n-cube graph is SO n -1 . Furthermore, we show that if the automorphism group of a graph contains a pair of disjoint automorphisms this graph has quantum symmetry.

Reçu le : 2018-11-14
Révisé le : 2019-07-15
Accepté le : 2019-09-18
Publié le : 2020-06-26
DOI : https://doi.org/10.5802/aif.3328
Classification : 46LXX,  20B25,  05CXX
Mots clés: graphes finis, automorphismes des graphes, groupes d’automorphismes, automorphismes quantiques, groupes quantiques, symétries quantiques
@article{AIF_2020__70_3_949_0,
     author = {Schmidt, Simon},
     title = {Quantum automorphisms of folded cube graphs},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {70},
     number = {3},
     year = {2020},
     pages = {949-970},
     doi = {10.5802/aif.3328},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2020__70_3_949_0/}
}
Schmidt, Simon. Quantum automorphisms of folded cube graphs. Annales de l'Institut Fourier, Tome 70 (2020) no. 3, pp. 949-970. doi : 10.5802/aif.3328. https://aif.centre-mersenne.org/item/AIF_2020__70_3_949_0/

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