Finite Euclidean graphs over rings

Medrano, A.; Myers, P.; Stark, H.; Terras, A.

doi:10.1090/S0002-9939-98-04294-4

Finite Euclidean graphs over rings
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by A. Medrano, P. Myers, H. M. Stark and A. Terras PDF

Proc. Amer. Math. Soc. 126 (1998), 701-710 Request permission

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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