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Testing Cayley graph densities

Goulnara N. ArzhantsevaVictor S. GubaMartin LustigJean-Philippe Préaux — 2008

Annales mathématiques Blaise Pascal

We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m -generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2 m . We test amenable and non-amenable...

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