树的变形与代数连通度

Deformation and Algebraic Connectivity of Weighted Trees

本文利用瓶颈矩阵的Perron值和代数连通度的二次型形式,系统地研究了当迁移或改变分支(边、点)和变动一些边的权重时无向赋权树的代数连通度的变化规律,认为代数连通度可用来描述树的边及其权重的某种中心趋势性.引入广义树和广义特征点概念,将Ⅱ型树转换成具有相同代数连通度的Ⅰ型树,使得树的代数连通度的讨论只须限于Ⅰ型树的研究即可.

In this paper,utilizing Perron value of bottleneck matrix for a branch based at a vertex and quadratic form of algebraic connectivity,change rules of algebraic connectivity on undirected weighted trees are studied roundly under changing or shafting branches（edges, vertices） and changing weights of edges.Algebraic connectivity could be considered as a measure of central tendency of edges and weights about a weighted tree.We introduce generalized tree and generalized characteristic vertex,and transform a TypeⅡtree into a TypeⅠtree with equal algebraic connectivity.Therefore,it only needs to investigate TypeⅠtrees when discuss algebraic connectivity of trees.