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arXiv · 1202.5484

Which finitely generated Abelian groups admit isomorphic Cayley graphs?

Clara Loeh
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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.

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Clara Loeh. 2012-02-24. Which finitely generated Abelian groups admit isomorphic Cayley graphs?. https://doi.org/10.1007/s10711-012-9761-x

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