Testing Cayley graph densities
Copyright policy )Testing Cayley graph densities
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 groups, and also groups for which amenability is unknown. In the latter class we focus on Richard Thompson’s group F .
- French National Centre for Scientific Research France
- University of Geneva Switzerland
- Aix-Marseille University France
- Centrale Marseille France
- Institut de Mathématiques de Marseille France
Generators, relations, and presentations of groups, Means on groups, semigroups, etc.; amenable groups, [MATH] Mathematics [math], finitely generated groups, Cayley graphs, 510, Graphs and abstract algebra (groups, rings, fields, etc.), Grafs, Teoria dels, Thompson group \(F\), Software, source code, etc. for problems pertaining to group theory, Density (toughness, etc.), amenability, computer-assisted group theory, Geometric group theory, ddc: ddc:510
Generators, relations, and presentations of groups, Means on groups, semigroups, etc.; amenable groups, [MATH] Mathematics [math], finitely generated groups, Cayley graphs, 510, Graphs and abstract algebra (groups, rings, fields, etc.), Grafs, Teoria dels, Thompson group \(F\), Software, source code, etc. for problems pertaining to group theory, Density (toughness, etc.), amenability, computer-assisted group theory, Geometric group theory, ddc: ddc:510
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