Spectrum of the Laplacian on a covering graph with pendant edges I: The one dimensional lattice and beyond
Spectrum of the Laplacian on a covering graph with pendant edges I: The one dimensional lattice and beyond
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带有下垂边的覆盖图上的拉普拉斯谱 I：一维晶格及其以外
DOI：
10.1016/j.laa.2013.09.017
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发表时间：
2013
影响因子：
1.1
通讯作者：
Akito Suzuki
中科院分区：
文献类型：
--
作者：
Reika Fukuizumi;Fouad Hadj Selem and Hiroaki Kikuchi;福泉麗佳;福泉麗佳;福泉麗佳;福泉麗佳;福泉麗佳;福泉麗佳;Akito Suzuki;Masaya Maeda and Kanako Suzuki;Akito Suzuki
在本文中，我们研究覆盖图，从d维整数格通过添加悬垂边。在d= 1的情形下，证明了图上的Laplacian有谱隙，并建立了Laplacian无特征值的充要条件.在d= 2的情况下，我们表明，存在一种安排的悬垂边，使拉普拉斯算子没有谱间隙。
In this paper, we examine covering graphs that are obtained from the d-dimensional integer lattice by adding pendant edges. In the case of d= 1, we show that the Laplacian on the graph has a spectral gap and establish a necessary and sufficient condition under which the Laplacian has no eigenvalues. In the case of d= 2, we show that there exists an arrangement of the pendant edges such that the Laplacian has no spectral gap.