Trees are connected acyclic graphs. Important properties of trees include having one fewer edges than vertices and the ability to designate a root node, creating a rooted tree. Basic tree terminology includes root, child, parent, siblings, leaves, height, and depth. Ordered trees are rooted trees where nodes are ordered left and right, such as in binary trees where each node has at most two children designated as left or right.

1. Trees
Basic terminology and proprery
By Bharati.C
M.Tech

2. Tree:
A tree is a connected acyclic graph.
Ex:
a b
d
g
c
f

3. Important property of tree
1. In a tree no. of edges one less than
vertices.
|E|=|V|-1
2. Rooted tree: select an arbitrary
vertex in a tree consider as the root so
called rooted tree.
It always placing top(level 0)

4. Ex:
i
b a
d
e
f
c
h g
Free tree
a
b d e
c g
h i
f
Rooted tree

5. Basic terminology of tree
• Root: top most node of the tree.
• Child: nodes next in the hierarchy.
• Parent: the node having further sub-branches is
called parent node.
• Siblings: nodes having same parent elements.
• Leaves: there are the last node of the tree.
• Height of tree: height of its root.
• Depth of tree: the no. of nodes on the path from
the root to the node.

6. Example:
a
b
e
c
d f
h
g
root
Parent nodes
siblings
leaves
Height of the tree=2
Depth of the tree=3

7. Ordered tree
an ordered tree is rooted tree which all its nodes
are ordered left and right.
Ex: binary tree
binary tree is an ordered tree which every node
has no more then two children and each
designated either left or right child.
Ordered tree always left node less then and
right child greater than parent node.

8. Example
10
8 12
7 9 11 13