planar graph, non planar graph , tree, twig branch

Planar Graph : A graph drawn on a 2 - dimensional plane is said to be planar if two branches do not intersect or cross at a point which is other than a node . 

Non Planar Graph : A graph drawn on a 2 - dimensional plane is said to be planar if two branches intersect or cross at a point which is other than a node .

Path : A set of elements that may be traversed in order without

passing through the same node twice.

Sub Graph : It is a sub set of branches and nodes of a graph. It is a  proper sub-graph if it contains branches and nodes less than those  on a graph. A sub graph can be just a node or only one branch of  the graph.

Tree & Twigs : A connected sub graph having all the nodes of a graph  without any loop is called a tree and branches of a tree are  called twigs.

Properties of Tree

There exists only one path between any pair of nodes in a tree

A tree contains all nodes of the graph

If n is the number of nodes of the graph, there are (n-1)  branches in the tree

Tree do not contain any loops

Every connected graph has at least one tree

Number of possible trees of a graph = A𝐴𝑇

Links or chord

The branches that are removed from the graph while forming a  tree are termed as links or chords

Links are complement of twigs.

Co - tree

The graph constituted with links is known as co-tree