Non-Ramanujancy of Euclidean graphs of order 2r Original Research Article

Graphs are attached to the n-dimensional space Z2rn where Z2r is the ring with 2r elements using an analogue of Euclidean distance. The graphs are shown to be non-Ramanujan for r=4. Comparisons are made with Euclidean graphs attached to Zprn for p an odd prime. The percentage of non-zero eigenvalues of the adjacency operator attached to these finite Euclidean graphs is shown to tend to zero as n tends to infinity.