等参数图的最大与最小距离树对及其在电网络分析中的应用

The Maximally and Minimally Distant Tree Pairs in the Equal Parameter Graphs and Their Applications in the Electrical Network Analysis

摘要: 本文推广了线图的树对及其距离的概念,提出了等参数图及其树对和树对之距离的概念。给出了等参数图中任一树对为一最大（或最小）距离树对的充分必要条件和相应的算法,讨论了等参数图中最大与最小距离树对在电网络分析中的应用,给出了网络图主划分算法1的对偶算法和电网络的最优调和分解算法。

Abstract: This paper develoPs the concepts of a pair of trees and their distance in a linear graph. The necessary and sufficient conditions for a maximally and minimally di'stant tree pair and the algorithms for finding a maximally and minimally distant tree pair are given. This paper also disccuses the applications of maximally and minimally distant tree pairs in equal parameter graphs in the electrical network analysis, and Presents the dual algorithm of Principal partition algithm 1 and the algrithm of oPtimal harmonious decomposition of electrical networks.