Graphs having no quantum symmetry

Teodor Banica (1, 2) , Julien Bichon (3) , Gaetan Chenevier (4, 5)

1 IMJ - Institut de Mathématiques de Jussieu
2 LEP - Laboratoire Émile Picard
3 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
4 DMA - Département de Mathématiques et Applications - ENS Paris
5 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: Quantum permutation group; Circulant graph.; Circulant graph

Domaines: Combinatoire [math.CO]; Algèbres quantiques [math.QA]

Teodor Banica, Julien Bichon, Gaetan Chenevier. Graphs having no quantum symmetry. 2006. ⟨hal-00218192⟩