论文标题
通过光谱括号
Isospectral graphs via spectral bracketing
论文作者
论文摘要
在本文中，我们开发了一种扰动技术来构建非同构离散图的家族，这些家族是标准（也称为归一化）laplacian及其无显着版本的标准（也称为归一化的）。我们将顶点收缩用作图形扰动和光谱括号，并带有辅助图，这些图具有具有高多重性的某些特征值。无需明确了解相应图的特征值或特征函数。我们通过介绍几个等谱图示例，包括模糊完整的两分图和从以前的示例获得的细分图来说明该方法。所有构建的示例也是相关等边度图上标准（Kirchhoff）laplacian的同一谱。
In this article, we develop a perturbative technique to construct families of non-isomorphic discrete graphs which are isospectral for the standard (also called normalised) Laplacian and its signless version. We use vertex contractions as a graph perturbation and spectral bracketing with auxiliary graphs which have certain eigenvalues with high multiplicity. There is no need to know explicitly the eigenvalues or eigenfunctions of the corresponding graphs. We illustrate the method by presenting several families of examples of isospectral graphs including fuzzy complete bipartite graphs and subdivision graphs obtained from the previous examples. All the examples constructed turn out to be also isospectral for the standard (Kirchhoff) Laplacian on the associated equilateral metric graph.
