Centered tree

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On the left a centered tree, on the right a bicentered one. The numbers shows the node's eccentricity.

In mathematics, a centered tree is a tree with only one center, and a bicentered tree is a tree with two centers. Any tree is either centered or bicentered.

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. For trees, however, there are only two possibilities:

1. The tree has precisely one center (centered trees).
2. The tree has precisely two centers (bicentered trees). In this case, the centers are always adjacent.

[edit] External links

• Eric W. Weisstein, Bicentered Tree at MathWorld.
• Eric W. Weisstein, Centered Tree at MathWorld.

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