# Oriented trees and ordered trees

I have this confusion regarding ordered and oriented trees. I know they are both rooted and in ordered trees, the order is important. So lets say I have four nodes

1,2,3,4 then it is given that the number of ordered trees is 5. How come this is true. I can create the following trees. Lets suppose the root is 1

  1            1          1          1
| | |        | | |      | | |      | | |
2 3 4        3 2 4      4 2 3      2 4 3

1   1
|   |
2   3
|   |
3   2
|   |
4   4


and the list goes on. I didn't understand this part. For oriented trees, I can say that the first four trees are equivalent and same and the bottom two trees are equali

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According to Cayley's formula, the number of oriented trees on $n$ vertices is $n^{n-1}$ (this is $n$ times the number given by the formula, since there are $n$ choices for the root). The number of ordered trees is surely larger. – Yuval Filmus Aug 28 '12 at 22:13

Ordered Tree

A tree where the children of each node have a designated order (not necessarily based on their value) and can be referred to specifically.

Oriented Tree

A tree used to represent hierarchical data. All edges are directed outward from a distinguished root node. also we can say,that oriented tree may contains at most undirected path between vertex,as in the following statment

A polytree or oriented tree is a directed graph with at most one undirected path between any two vertices. In other words, a polytree is a directed acyclic graph for which there are no undirected cycles either.

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It might be more helpful to explain more details instead of only the definitions. – Gigili May 5 '12 at 14:08
ok i see thanks for advice – dato datuashvili May 5 '12 at 14:23