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Graphs having no quantum symmetry. (English) Zbl 1178.05047
Summary: 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.
##### MSC:
 05C25 Graphs and abstract algebra 20B25 Finite automorphism groups of miscellaneous structures 16T20 Ring-theoretic aspects of quantum groups 46L05 General theory of ${C}^{*}$-algebras
##### Keywords:
quantum permutation group; circulant graph