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.