Cogrowth of Regular Graphs

dc.contributor.author	Northshield, Sam
dc.date.accessioned	2018-04-09T18:47:32Z
dc.date.accessioned	2020-06-22T14:35:29Z
dc.date.available	2018-04-09T18:47:32Z
dc.date.available	2020-06-22T14:35:29Z
dc.date.issued	1992
dc.identifier.citation	Northshield, S. (1992). Cogrowth of Regular Graphs. Proceedings of the American Mathematical Society, 116(1). http://doi.org/10.1090/S0002-9939-1992-1120509-0	en_US
dc.identifier.uri	http://hdl.handle.net/20.500.12648/1109
dc.description	This article has been published in the September 1992 issue of Proceedings of the American Mathematical Society.	en_US
dc.description.abstract	Let G be a d-regular graph and T the covering tree of G. We define a cogrowth constant of G in T and express it in terms of the first eigenvalue of the Laplacian on G. As a corollary, we show that the cogrowth constant is as large as possible if and only if the first eigenvalue of the Laplacian on G is zero. Grigorchuk's criterion for amenability of finitely generated groups follows.	en_US
dc.language	en_US	en_US
dc.publisher	Proceedings of the American Mathematical Society	en_US
dc.subject	Regular graph	en_US
dc.subject	covering tree	en_US
dc.subject	amenable group	en_US
dc.subject	random walk	en_US
dc.title	Cogrowth of Regular Graphs	en_US
dc.type	Article	en_US
refterms.dateFOA	2020-06-22T14:35:29Z
dc.description.institution	SUNY Plattsburgh

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