标题： 球面对称图的谱分析 显示英文标题

标题： Spectral Analysis of Certain Spherically Homogeneous Graphs

摘要： 我们研究了根图上的算子，这些图具有一定的球面齐次性。 这类图被称为路径交换图，并且允许邻接矩阵和拉普拉斯算子分解为雅可比矩阵的直和，这些雅可比矩阵反映了图的结构。 因此，可以通过雅可比矩阵的成熟理论来分析邻接矩阵和拉普拉斯算子的谱性质。 对于一些例子（包括反树），我们明确地推导出这种分解，并展示由图的几何结构引起的光谱行为的动物园。 特别是，这些例子表明，在粗糙同胚下，光谱类型根本不是稳定的。 显示英文摘要

摘要： We study operators on rooted graphs with a certain spherical homogeneity. These graphs are called path commuting and allow for a decomposition of the adjacency matrix and the Laplacian into a direct sum of Jacobi matrices which reflect the structure of the graph. Thus, the spectral properties of the adjacency matrix and the Laplacian can be analyzed by means of the elaborated theory of Jacobi matrices. For some examples which include antitrees, we derive the decomposition explicitly and present a zoo of spectral behavior induced by the geometry of the graph. In particular, these examples show that spectral types are not at all stable under rough isometries.