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Template:Short description Template:Use American English Template:Use mdy dates
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 Template:Mvar is defined as the greatest distance from Template:Mvar 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, Template:Harvtxt 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.[1]
Notes
- ↑ Script error: No such module "Footnotes"., Theorem 4.2
References
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External links
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