Definition:Center (Graph Theory)

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

• Two nodes are left, joined by a single edge.

If one node is left, it is called the center of the tree.

Such a tree is called a central tree.

If two nodes are left, joined by a single edge, this is called the bicenter of the tree.

Such a tree is called a bicentral tree.

From Tree has Center or Bicenter, every tree is either central or bicentral, but not both.

Note

The UK English spelling of this is "centre".