Definition:Center of Tree
(Redirected from Definition:Bicenter of Tree)
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This page is about Center in the context of Graph Theory. For other uses, see Center.
Definition
Take a tree, and remove all the nodes whose degree is $1$, along with all their incident edges.
Repeat the process until either:
- One node is left
or:
If one node is left, it is called the center of the tree.
If two nodes are left, joined by a single edge, this is called the bicenter of the tree.
Central Tree
A tree $T$ is central if and only if it has a center.
Bicentral Tree
A tree $T$ is bicentral if and only if it has a bicenter.
Also see
- Tree has Center or Bicenter, proving every tree has either a center or a bicenter, but not both.
Linguistic Note
The British English spelling of center is centre.
The convention on $\mathsf{Pr} \infty \mathsf{fWiki}$ is to use the American English spelling center, but it is appreciated that there may be lapses.