Geometriae Dedicata

, Volume 164, Issue 1, pp 97–111 | Cite as

Which finitely generated Abelian groups admit isomorphic Cayley graphs?

Original Paper

Abstract

We show that Cayley graphs of finitely generated Abelian groups are rather rigid. As a consequence we obtain that two finitely generated Abelian groups admit isomorphic Cayley graphs if and only if they have the same rank and their torsion parts have the same cardinality. The proof uses only elementary arguments and is formulated in a geometric language.

Keywords

Cayley graphs Graph isomorphisms Rigidity 

Mathematics Subject Classification (2010)

05C25 05C63 20F65 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany

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