Centered tree



In the mathematical subfield of graph theory, a centered tree is a tree with only one center, and a bicentered tree is a tree with two centers.

Given a graph, the eccentricity of a vertex $v$ is defined as the greatest distance from $v$ to any other vertex. A center of a graph is a vertex with minimal eccentricity. A graph can have an arbitrary number of centers. However, has proved that for trees, there are only two possibilities: A proof of this fact is given, for example, by Harary.
 * 1) The tree has precisely one center (centered trees).
 * 2) The tree has precisely two centers (bicentered trees). In this case, the two centers are adjacent.