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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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IMPACT FACTOR 2016 (Central European Journal of Mathematics): 0.489

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Volume 13, Issue 1 (Apr 2015)


Two bounds on the noncommuting graph

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
/ Francesco G. Russo
  • Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch 7701, Cape Town, South Africa
Published Online: 2015-04-15 | DOI: https://doi.org/10.1515/math-2015-0027


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.

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


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About the article

Received: 2014-08-11

Accepted: 2014-03-07

Published Online: 2015-04-15

Citation Information: Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0027.

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©2015 Stefano Nardulli and Francesco G. Russo. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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