Finite Euclidean graphs over rings
Authors:
A. Medrano, P. Myers, H. M. Stark and A. Terras
Journal:
Proc. Amer. Math. Soc. 126 (1998), 701-710
MSC (1991):
Primary 11T23; Secondary 05C25
DOI:
https://doi.org/10.1090/S0002-9939-98-04294-4
MathSciNet review:
1443395
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Abstract | References | Similar Articles | Additional Information
Abstract: We consider graphs attached to , where
, for an odd prime
, using an analogue of the Euclidean distance. These graphs are shown to be mostly non-Ramanujan, in contrast to the case of Euclidean graphs over finite fields.
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Additional Information
A. Medrano
Affiliation:
Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
P. Myers
Affiliation:
Department of Mathematics, University of California, Santa Cruz, California 95064
Email:
pmyers@cats.ucsc.edu
A. Terras
Email:
aterras@ucsd.edu
DOI:
https://doi.org/10.1090/S0002-9939-98-04294-4
Keywords:
Euclidean graph,
Ramanujan graph,
Kloosterman sums over rings
Received by editor(s):
September 11, 1996
Communicated by:
Dennis A. Hejhal
Article copyright:
© Copyright 1998
American Mathematical Society