Two bounds on the noncommuting graph
Keyword(s):
AbstractErdős 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.
2006 ◽
Vol 96
(2)
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pp. 302-312
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Keyword(s):
1956 ◽
Vol 52
(1)
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pp. 5-11
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2008 ◽
Vol 22
(4)
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pp. 1381-1392
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1983 ◽
Vol 34
(1)
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pp. 48-57
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1971 ◽
Vol 69
(3)
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pp. 401-407
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