Maximum-Path Leaves Relative to Vertices and the Vertex One Center of a Spanning211 Tree: An Enumeration and Analysis of Configurations

摘要

This paper enumerates the configurations of a pair of vertices (one of which is a211u001eleaf) relative to the unique vertex one center and the leaf of greatest path 211u001elength from this center in a spanning tree of a graph. From this enumeration, it 211u001edemonstrates that the vertex one center is between the vertex and the leaf of 211u001egreatest path length from the vertex for every such pair of vertices. Using this 211u001eresult this paper develops an algorithm for the optimal reconfiguration of a tree 211u001einfrastructure required to recover from the failure of a network element.