Discrete Mathematics

Mainly a graph consists of two components:
The set of the vertices is denoted by V. Sometimes it is also called nodes or points.
The set of edges is denoted by e. i.e. when we join the pair of vertices, then a line joining the points is called the edges. Sometimes it also called arcs or single lines.
If in a graph G, the numbers of vertices are V and numbers of edges are e, then a graph is written as
G = (V, e)
Graph = (Number of Vertices, Number of Edges)
Examples of a Graph


Sub Graph A graph h is called a sub graph of H if all the vertices and all the edges of h are in H, and each edge of h has the same end vertices in h as in H.

Draw the sub-graphs of a given graph

Solution : A sub graph by deleting the edge between v4 and V5.

A sub graph by deleting v4.

A sub graph by deleting the edge between v2 and V3.

A sub graph by deleting Vertex V1, an edge between v2 and V5, and V3 and V5.

A sub graph by deleting an edge between v2 and V3, V2 and V4, and V3 and V4.

Draw the sub-graphs of a given graph

Solution : A sub graph by deleting Vertex V5

A sub graph by deleting an edge between V1 and V5, V4 and V6, and Vertex V5.

Determine the sub graph by deleting the vertex, G – v1, G – v8, G – v2, G – V2, V4 of the graph G = (V, E)

Solution: After deleting some edges and vertices from graphs, the subgraphs are G – v1, G – v8, G – v2, G – V2, V4

Sub Graph: G – V1:

Sub Graph: G – v2

Sub Graph: G – V3:

Sub Graph: G – V2, V4