Maximum-Path Leaves Relative to Vertices and the Vertex One Center of a Spanning Tree: An Enumeration and Analysis of Configurations
L.J. Dowell · 1998
This paper enumerates the configurations of a pair of vertices (one of which is a leaf) relative to the unique vertex one center and the leaf of greatest path length from this center in a spanning tree of a graph. From this enumeration, it demonstrates that the vertex one center is between the vertex and the leaf of greatest path length from the vertex for every such pair of vertices. Using this result this paper develops an algorithm for the optimal reconfiguration of a tree infrastructure required to recover from the failure of a network element.