Centered tree
Tree graph with only one center
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, Jordan (1869) 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.
Sources and credits
This article is adapted from the Wikipedia article “Centered tree”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.
Images, from Wikimedia Commons:
- Centered tree.gif by Claudio Rocchini, CC BY 2.5
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