Which finitely generated Abelian groups admit isomorphic Cayley graphs?
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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.
KeywordsCayley graphs Graph isomorphisms Rigidity
Mathematics Subject Classification (2010)05C25 05C63 20F65
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- 3.Ryabchenko, A.A.: Isomorphisms of Cayley graphs of a free abelian group. (Russian. Russian summary). Sibirsk. Mat. Zh. 48 (5), 1142–1146, 2007. translation in Siberian Math. J. 48 (5), 919–922 (2007)Google Scholar
- 5.Cayley graphs of finitely generated groups. Discussion on mathoverflow. http://mathoverflow.net/questions/18766/cayley-graphs-of-finitely-generated-groups. Accessed 23 Feb 2012