Cayley graphs with few automorphisms: the case of infinite groups

Paul-Henry Leemann; Mikael de la Salle

doi:10.5802/ahl.118

Cayley graphs with few automorphisms: the case of infinite groups

Paul-Henry Leemann
, Mikael de la Salle

Université de Lyon

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 language	English
Pages (from-to)	73-92
Journal	Annales Henri Lebesgue
Volume	5
DOIs	https://doi.org/10.5802/ahl.118
Publication status	Published - Sept 2022

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10.5802/ahl.118

2 Invited talk
1 Presentation at conference/workshop/seminar
1 Research visit

Taiwan University
Leemann, P.-H. (Visiting researcher)
1 Jun 2026 → 5 Jun 2026
Activity: Research visit
Rigidity of Cayley graphs
Leemann, P.-H. (Speaker)
10 Nov 2023
Activity: Talk or presentation › Invited talk
Random walks on infinite groups: some applications
Leemann, P.-H. (Speaker)
16 Oct 2023
Activity: Talk or presentation › Invited talk

Cite this

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title = "Cayley graphs with few automorphisms: the case of infinite groups",

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.",

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AB - 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.

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Cayley graphs with few automorphisms: the case of infinite groups

Abstract

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Activities

Taiwan University

Rigidity of Cayley graphs

Random walks on infinite groups: some applications

Cite this