基于网络拓扑图的树的代数连通度

代数图谱理论方法在网络设计中发挥重要作用。网络拓扑图的Laplacian矩阵的谱与网络的同步能力有关，代数连通度就是一个刻画同步能力的重要参数。采用移接变形方法，讨论了树的代数连通度和直径之间的关系，获得了下面的结论：当树的顶点数固定时，树的代数连通度随着树的直径的增加而减少。进一步地，讨论了树的代数连通度的上界和下界。

Algebraic connectivity of trees based on network topology

Algebraic graph theory methods play an important role in the network design. Spectrum of Laplacian matrix is associated with the synchronous ability of network. The algebraic connectivity is a depict important parameter of synchronous ability. In this paper, using a grafting method, it discusses the relationship between algebraic connectivity and diameter of a tree. For a special class of trees, the algebraic connectivity of the tree with a fixed number of vertices, is decreasing along with the increase of diameter. Moreover, using the Cauchy-Schwarz inequality as a guide, it also obtains bounds for the algebraic connectivity of a tree.