关键词: 树, 拉普拉斯矩阵, 代数连通度, 直径

Abstract: 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.

Key words:  tree, Laplace matrix, algebraic connectivity, diameter