Graphs having no quantum symmetry

Banica, Teodor; Bichon, Julien; Chenevier, Gaëtan

doi:10.5802/aif.2282

Graphs having no quantum symmetry
[Graphes n’ayant pas de symétrie quantique]

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)

Annales de l'Institut Fourier, Tome 57 (2007) no. 3, pp. 955-971.

Résumé
Abstract

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 $p ≫ k$ 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 $p ≫ k$ the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.

EuDML MR Zbl

DOI : 10.5802/aif.2282

Classification : 16W30, 05C25, 20B25
Keywords: Quantum permutation group, circulant graph
Mot clés : groupe quantique de permutation, graphe circulant

Affiliations des auteurs :

Banica, Teodor ¹ ; Bichon, Julien ² ; Chenevier, Gaëtan ³

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     title = {Graphs having no quantum symmetry},
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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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