A rooted tree is a tree with a node named as root of the tree. A tree which does not has root node, is sometimes called a free tree/unrooted tree (A tree which does not have a root node). Although the term “tree” generally refers to a free tree.

###### Terminologies used:

**Root:**Node at the top of the tree.**Parent:**Any node, except root has exactly one edge running upward to another node. The node above it is called it’s parent.

Example: in fig. 1 (last row, 1^{st}tree) parent of node B is node A, parent of node C is node B.**Child:**Any node may have one or more lines running downward to other nodes. Nodes below are children.

Example: in fig. 1 (last row, 2^{nd}tree) nodes B and C are children of node A and node D is children of node B.**Siblings:**A group of nodes with the same parent.**Leaf:**A node that has no children.

Example: in fig. 1 (last row, 2^{nd}tree) nodes D and C are leaf nodes.**Subtree:**Any node can be considered to be the root of a subtree, which consists of its children and its childrenâ€™s children and so on.

The numbers of rooted trees on n nodes for n=1, 2, … are 1, 1, 2, 4, 9, 20, 48, 115, 286….. (sequence A000081 in the OEIS).