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

Access to Document

10.5802/ahl.118

2 Invited talk
1 Presentation at conference/workshop/seminar

Rigidity of Cayley graphs
Paul-Henry Leemann (Speaker)
10 Nov 2023
Activity: Talk or presentation › Invited talk
Random walks on infinite groups: some applications
Paul-Henry Leemann (Speaker)
16 Oct 2023
Activity: Talk or presentation › Invited talk
Cayley graphs with few automorphisms
Paul-Henry Leemann (Speaker)
23 Sept 2022
Activity: Talk or presentation › Presentation at conference/workshop/seminar

Cite this

@article{1d2dff6e485445c9b9fd5508c132ec21,

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.",

author = "Paul-Henry Leemann and {de la Salle}, Mikael",

year = "2022",

doi = "10.5802/ahl.118",

language = "English",

volume = "5",

pages = "73--92",

journal = "Annales Henri Lebesgue",

issn = "2644-9463",

}

TY - JOUR

T1 - Cayley graphs with few automorphisms: the case of infinite groups

AU - Leemann, Paul-Henry

AU - de la Salle, Mikael

PY - 2022

Y1 - 2022

N2 - 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.

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.

U2 - 10.5802/ahl.118

DO - 10.5802/ahl.118

M3 - Article

SN - 2644-9463

VL - 5

SP - 73

EP - 92

JO - Annales Henri Lebesgue

JF - Annales Henri Lebesgue

ER -

Cayley graphs with few automorphisms: the case of infinite groups

Abstract

Access to Document

Fingerprint

Activities

Rigidity of Cayley graphs

Random walks on infinite groups: some applications

Cayley graphs with few automorphisms

Cite this