Two bounds on the noncommuting graph
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 reaso...
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De Gruyter
2015-04-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2015-0027 |
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doaj-5c7d839475e949d4be55003cb829518d2021-09-06T19:20:07ZengDe GruyterOpen Mathematics2391-54552015-04-0113110.1515/math-2015-0027math-2015-0027Two bounds on the noncommuting graphNardulli Stefano0Russo Francesco G.1Instituto 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, BrasilDepartment of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch 7701, Cape Town, South AfricaErdős 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.https://doi.org/10.1515/math-2015-0027noncommuting graph sobolev–poincaré inequality laplacian operator isoperimetric inequality |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Nardulli Stefano Russo Francesco G. |
| spellingShingle |
Nardulli Stefano Russo Francesco G. Two bounds on the noncommuting graph Open Mathematics noncommuting graph sobolev–poincaré inequality laplacian operator isoperimetric inequality |
| author_facet |
Nardulli Stefano Russo Francesco G. |
| author_sort |
Nardulli Stefano |
| title |
Two bounds on the noncommuting graph |
| title_short |
Two bounds on the noncommuting graph |
| title_full |
Two bounds on the noncommuting graph |
| title_fullStr |
Two bounds on the noncommuting graph |
| title_full_unstemmed |
Two bounds on the noncommuting graph |
| title_sort |
two bounds on the noncommuting graph |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2015-04-01 |
| description |
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. |
| topic |
noncommuting graph sobolev–poincaré inequality laplacian operator isoperimetric inequality |
| url |
https://doi.org/10.1515/math-2015-0027 |
| work_keys_str_mv |
AT nardullistefano twoboundsonthenoncommutinggraph AT russofrancescog twoboundsonthenoncommutinggraph |
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1717777279646433280 |