Unoriented tree

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Undirected tree with four inner nodes (black) and five leaves (white)

In graph theory, an undirected tree is a special tree whose edges have no particular direction. In contrast to rooted trees with edge directions, undirected trees do not have an excellent root . It is only possible to identify leaves that are characterized by the fact that they only have exactly one neighbor , whose degree is exactly 1. As order here refers to the maximum level of the tree. As internal nodes is referred to all of the nodes which are not leaves.

Pairwise equivalent characterizations

Undirected trees are simple connected graphs that satisfy one of the following equivalent conditions.

  1. You don't have a circle .
  2. Any two different nodes are connected by exactly one path .
  3. The number of nodes is 1 greater than the number of edges .