Cayley graphs with few automorphisms: the case of infinite groups

Paul-Henry Leemann, Mikael de la Salle

Published 2020-10-12Version 1

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.