The t-Graphs over Finitely Generated Groups and the Minkowski Metric

Cayley graphs of finitely generated groups

There does not exist a Borel choice of generators for each finitely generated group which has the property that isomorphic groups are assigned isomorphic Cayley graphs.

Neighbourhood Graphs of Cayley Graphs for Finitely-generated Groups

In this short note the neighbourhood graph of a Cayley graph is considered. It has as nodes a symmetric generating set of a finitely-generated group Γ. Two nodes are connected by an edge if one is obtained from the other by multiplication on the right by one of the generators. Two necessary conditions on the graphs are shown. One is a condition on the degrees of the graph, the other concerns co...

Finitely Generated Abelian Groups

Finitely Generated Semiautomatic Groups

The present work shows that Cayley automatic groups are semiautomatic and exhibits some further constructions of semiautomatic groups and in particular shows that every finitely generated group of nilpotency class 3 is semiautomatic.

Which Finitely Generated Abelian Groups Admit Isomorphic Cayley Graphs?

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.