Oriented trees and ordered trees

Question

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

Answer 1

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.