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Article Dans Une Revue Annales Henri Lebesgue Année : 2022

Cayley graphs with few automorphisms: the case of infinite groups

Résumé

We characterize the finitely generated groups that admit a Cayley graph whose only automorphisms are the translations, confirming a conjecture by Watkins from 1976. The proof relies on random walk techniques. As a consequence, every finitely generated group admits a Cayley graph with countable automorphism group. We also treat the case of directed graphs.

Dates et versions

hal-02967126 , version 1 (14-10-2020)

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Citer

Paul-Henry Leemann, Mikael de la Salle. Cayley graphs with few automorphisms: the case of infinite groups. Annales Henri Lebesgue, 2022, 5, pp.73-92. ⟨10.5802/ahl.118⟩. ⟨hal-02967126⟩
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