Non-Ramanujancy of Euclidean graphs of order 2r

被引：3

作者：

DeDeo, MR ^{[1
]}

机构：

[1] Dept Math & Stat, Jacksonville, FL 32224 USA

来源：

DISCRETE MATHEMATICS | 2003年 / 265卷 / 1-3期

关键词：

Ramanujan graph; Euclidean graph; spectra of graphs;

D O I：

10.1016/S0012-365X(02)00621-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Graphs are attached to the n-dimensional space Z(2r)'' where Z(2r) is the ring with 2(r) 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 Z(pr)'' 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. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：45 / 57

页数：13

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