Quantum automorphism groups of vertex-transitive graphs of order <= 11

Teodor Banica (1, 2) , Julien Bichon (3)

1 IMJ - Institut de Mathématiques de Jussieu
2 LEP - Laboratoire Émile Picard
3 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We study quantum automorphism groups of vertex-transitive graphs having less than 11 vertices. With one possible exception, these can be obtained from cyclic groups ${\mathbb Z}_n$, symmetric groups $S_n$ and quantum symmetric groups $\mathcal Q_n$, by using various product operations. The exceptional case is that of the Petersen graph, and we present some questions about it.

Mots clés: Quantum permutation group; Transitive graph

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

Teodor Banica, Julien Bichon. Quantum automorphism groups of vertex-transitive graphs of order <= 11. 2006. ⟨hal-00217834⟩