Actions for Maximum-Path Leaves Relative to Vertices and the Vertex One Center of a Spanning Tree [electronic resource] : An Enumeration and Analysis of Configurations
Maximum-Path Leaves Relative to Vertices and the Vertex One Center of a Spanning Tree [electronic resource] : An Enumeration and Analysis of Configurations
Published
Washington, D.C. : United States. Dept. of Defense, 1998. Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
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.