图的(规范)拉普拉斯特征值与图的若干参数

(Normalized)Laplacian Eigenvalues of a Graph and Its Structural Parameters

用图的(规范)拉普拉斯特征值去反映图的结构特征是图谱理论研究的热点。分别给出了图的拉普拉斯特征值与其匹配数、点连通度以及边连通度之间的关系;同时也给出了图的规范拉普拉斯特征值与其韧度的关系,部分结论推广或改进了已有的结论。

Using the(Normalized)Laplacian eigenvalues of a graph to reflect its structural properties is a focused issue in the study of spectral graph theory.In this paper,the relationships between the Laplacian eigenvalues of a graph and its matching number,vertex-connectivity and edge-connectivity are explored,respectively,as well as the relationship between the normalized Laplacian eigenvalues of a graph and its toughness.Some of the results extend or improve the existing results.