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- 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: 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. A proof of this fact is given, for example, by Harary. (en)
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- Bicentered Tree (en)
- Centered Tree (en)
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- BicenteredTree (en)
- CenteredTree (en)
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- 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: 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. (en)
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