Spectral structure of the Laplacian on a covering graph

被引：38

作者：

Higuchi, Yusuke ^{[1
]}

Nomura, Yuji ^{[2
]}

机构：

[1] Showa Univ, Coll Arts & Sci, Math Labs, Fujiyoshida, Yamanashi 4030005, Japan

[2] Tokyo Inst Technol, Dept Math, Meguro Ku, Tokyo 1528551, Japan

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2009年 / 30卷 / 02期

关键词：

D O I：

10.1016/j.ejc.2008.03.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the spectral structure of the discrete Laplacian on an infinite graph. We show that, for a finite graph including a certain kind of a family of cycles, the spectrum of the Laplacian on its homology universal covering graph has band structure and no eigenvalues; furthermore it is purely absolutely continuous. Interesting examples that illustrate our theorems are also exhibited. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：570 / 585

页数：16

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