# American Institute of Mathematical Sciences

2003, 2003(Special): 678-687. doi: 10.3934/proc.2003.2003.678

## Quasi-regular graphs, cogrowth, and amenability

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

Received  September 2002 Revised  March 2003 Published  April 2003

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.
Citation: Sam Northshield. Quasi-regular graphs, cogrowth, and amenability. Conference Publications, 2003, 2003 (Special) : 678-687. doi: 10.3934/proc.2003.2003.678
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