Quasi-regular graphs, cogrowth, and amenability

Sam Northshield

doi:10.3934/proc.2003.2003.678

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2003, Volume 2003: 678-687. Doi: 10.3934/proc.2003.2003.678 open access

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Quasi-regular graphs, cogrowth, and amenability

Sam Northshield^1,

1.
Dept. of Mathematics, Plattsburgh State University, Plattsburgh, NY 12901

Received: August 31, 2002

Revised: February 28, 2003

Published: March 2003

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Abstract

We extend Grigrochuk’s cogrowth criterion for amenability of groups to the case of non-regular graphs for which a certain regularity condition is satisfied. The proof involves generalized Laplacians which are inverses of growth series and whose determinants are closely related to zeta functions of graphs.

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Mathematics Subject Classification: Primary 31C20; Secondary 31C35, 43A07, 31C05, 39A12.

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