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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1443395
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Abstract: We consider graphs attached to $(\mathbb {Z}/q\mathbb {Z})^n$, where $q=p^r$, for an odd prime $p$, 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: http://dx.doi.org/10.1090/S0002-9939-98-04294-4
PII: S 0002-9939(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