Cayley graphs with few automorphisms: the case of infinite groups

Paul-Henry Leemann, Mikael de la Salle

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)73-92
JournalAnnales Henri Lebesgue
Volume5
DOIs
Publication statusPublished - 2022

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Leemann, P.-H., & de la Salle, M. (2022). Cayley graphs with few automorphisms: the case of infinite groups. Annales Henri Lebesgue, 5, 73-92. https://doi.org/10.5802/ahl.118