Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
TESTING CAYLEY GRAPH DENSITIES G. N. Arzhantseva, V. S. Guba, M. Lustig, and J.-Ph. Pr eaux
 

Summary: TESTING CAYLEY GRAPH DENSITIES
G. N. Arzhantseva, V. S. Guba, M. Lustig, and J.-Ph. Pr eaux
Abstract. We present a computer-assisted analysis of combinatorial properties of the Cayley
graphs of certain nitely generated groups: Given a group with a nite 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 nite subgraph. It is known that
an m-generated group is amenable if and only if the density of the corresponding Cayley
graph equals to 2m. We test amenable and non-amenable groups, and also groups for which
amenability is unknown. In the latter class we focus on Richard Thompsons group F .
G. N. Arzhantseva Section de Math ematiques, Universit e de Gen eve, C.P. 64, CH-1211
Gen eve 4, Suisse.
E-mail: Goulnara.Arjantseva@math.unige.ch
V. S. Guba Department of mathematics, Vologda State University, 6 S. Orlov St., Vologda
160600, Russia.
E-mail: guba@uni-vologda.ac.ru
M. Lustig LATP, UMR CNRS 6632, Math ematiques, Universit e d'Aix-Marseille III, Av-
enue Escadrille Normandie-Niemen, 13397 Marseille 20, France
E-mail: martin.lustig@univ.u-3mrs.fr
J.-Ph. Pr eaux Centre de recherche de l' ecole de lair Ecole de l'air, F-13661, Salon de
Provence air & Centre de Mathmatiques et d'Informatique, Universit de Provence, 39, rue

  

Source: Arzhantseva, Goulnara N. - Section de Mathématiques, Université de Genève

 

Collections: Mathematics