Two bounds on the noncommuting graph

• Autorzy: Stefano Nardulli , Francesco G. Russo
• Języki publikacji: EN

Abstrakty

EN

Erdős introduced the noncommuting graph in order to study the number of commuting elements in a finite group. Despite the use of combinatorial ideas, his methods involved several techniques of classical analysis. The interest for this graph has become relevant during the last years for various reasons. Here we deal with a numerical aspect, showing for the first time an isoperimetric inequality and an analytic condition in terms of Sobolev inequalities. This last result holds in the more general context of weighted locally finite graphs.

Słowa kluczowe

EN

Noncommuting graph; Sobolev–Poincaré inequality; Laplacian operator; Isoperimetric inequality

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

zaakceptowano

2014-03-07

otrzymano

2014-08-11

online

2015-04-15

Twórcy

autor

Stefano Nardulli

• Instituto de Matemática, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149,
  Centro de Tecnologia, Bloco C, Cidade Universitária, Ilha do Fundão, Caixa Postal 68530, 21941-909, Rio de Janeiro, Brasil

autor

Francesco G. Russo

• Department of Mathematics and Applied Mathematics, University of Cape Town,
  Private Bag X1, Rondebosch 7701, Cape Town, South Africa

Bibliografia

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Identyfikatory

DOI

10.1515/math-2015-0027