Graphs having no quantum symmetry

Banica, Teodor; Bichon, Julien; Chenevier, Gaëtan

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

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