Graphs having no quantum symmetry
[Graphes n’ayant pas de symétrie quantique]
Annales de l'Institut Fourier, Tome 57 (2007) no. 3, pp. 955-971.

On considère des graphes circulants ayant p sommets, avec p premier. A un tel graphe on associe un certain nombre k, qu’on appelle type du graphe. On montre que pour pk le graphe n’a pas de symétrie quantique, dans le sens où son groupe quantique d’automorphismes est réduit à son groupe classique d’automorphismes.

We consider circulant graphs having p vertices, with p prime. To any such graph we associate a certain number k, that we call type of the graph. We prove that for pk the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.

DOI : 10.5802/aif.2282
Classification : 16W30, 05C25, 20B25
Keywords: Quantum permutation group, circulant graph
Mot clés : groupe quantique de permutation, graphe circulant
Banica, Teodor 1 ; Bichon, Julien 2 ; Chenevier, Gaëtan 3

1 Université Toulouse 3 Département de mathématiques 118, route de Narbonne 31062 Toulouse (France)
2 Université de Pau Département de mathématiques 1, avenue de l’université 64000 Pau (France)
3 Université Paris 13 Département de mathématiques 99, avenue J-B. Clément 93430 Villetaneuse (France)
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Banica, Teodor; Bichon, Julien; Chenevier, Gaëtan. Graphs having no quantum symmetry. Annales de l'Institut Fourier, Tome 57 (2007) no. 3, pp. 955-971. doi : 10.5802/aif.2282. http://www.numdam.org/articles/10.5802/aif.2282/

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