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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access April 15, 2015

Two bounds on the noncommuting graph

  • Stefano Nardulli and Francesco G. Russo
From the journal Open Mathematics

Abstract

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.

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Received: 2014-8-11
Accepted: 2014-3-7
Published Online: 2015-4-15

©2015 Stefano Nardulli and Francesco G. Russo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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