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 is defined as the greatest distance from 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:
# The tree has precisely one center (centered trees).
# The tree has precisely two centers (bicentered trees). In this case, the two centers are adjacent.
A proof of this fact is given, for example, by Harary., Theorem 4.2

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Trees (graph theory)

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