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

Department of Pure Mathematics

Université de Lyon

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	73-92
Journal	Annales Henri Lebesgue
Volume	5
DOIs	https://doi.org/10.5802/ahl.118
Publication status	Published - 2022

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10.5802/ahl.118

Rigidity of Cayley graphs
Paul-Henry Leemann (Speaker)
10 Nov 2023
Activity: Talk or presentation › Presentation at conference/workshop/seminar
Random walks on infinite groups: some applications
Paul-Henry Leemann (Speaker)
16 Oct 2023
Activity: Talk or presentation › Presentation at conference/workshop/seminar

Cite this

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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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DO - 10.5802/ahl.118

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VL - 5

SP - 73

EP - 92

JO - Annales Henri Lebesgue

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Cayley graphs with few automorphisms: the case of infinite groups

Abstract

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Activities

Rigidity of Cayley graphs

Random walks on infinite groups: some applications

Cite this