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The Frucht property in the quantum group setting

Part of: Graph theory Permutation groups

Published online by Cambridge University Press:  29 November 2021

T. Banica Open the ORCID record for T. Banica [Opens in a new window]  and
J.P. McCarthy Open the ORCID record for J.P. McCarthy [Opens in a new window]
T. Banica
Affiliation:
Department of Mathematics, University of Cergy-Pontoise, Cergy-Pontoise, France. e-mail: teo.banica@gmail.com
J.P. McCarthy
Affiliation:
Department of Mathematics, Munster Technological University, Cork, Ireland. e-mail: jeremiah.mccarthy@mtu.ie
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Abstract

A classical theorem of Frucht states that any finite group appears as the automorphism group of a finite graph. In the quantum setting, the problem is to understand the structure of the compact quantum groups which can appear as quantum automorphism groups of finite graphs. We discuss here this question, notably with a number of negative results.

Keywords

Quantum permutationQuantum automorphism

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 3 , September 2022 , pp. 603 - 633
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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