n discrete mathematics, a graph is a collection of points, called vertices, and lines between those points, called edges. There are many different types of graphs, such as connected and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs.

1. Graph : Discrete
Mathematics
Presentation
Nasir Hussain
Quaid-i-Azam University Islamabad. BS Computer Science 24

2. GRAPH
 Definition
A graph G = (V ,E) consists of V , a nonempty set of vertices (or nodes) and E, a
set of edges. Each edge has either one or two vertices associated with it, called its
endpoints. An edge is said to connect its endpoints.
 Computer Network
Now suppose that a network is made up of data centers and communication links
between computers. We can represent the location of each data center by a point
and each communications link by a line segment.

3. Graph of Computer Network

4. Category of Graph
 On the base of definition there are two main category of graph:
1. Infinite Graph:
A graph with an infinite vertex set or an infinite
number of edges is called an infinite graph.
2. Finite Graph:
A graph with a finite vertex set and a finite edge set is called a finite graph.
Here we only consider finite graph.

5. Adjacent Vertex
 If two vertices are joined by the same edge, they are called adjacent vertex

6. Adjacent Edge
 If two edge are incident on same vertex they are called adjacent edge

7. Parallel edge
 When more than one edge associated with the same pair of vertices such edges
are called parallel edges.

8. Types of Graph
A. UN-DIRECTED GRAPH:
A set of object that are connected together, where all
the edges are bidirectional.
1. Simple Graph
2. Multi Graph
3. Pseudo Graph
B. DIRECTED GRAPH:
A. Simple Directed Graph
B. Directed Multigraph
C. MIXED GRAPH.

9. SIMPLE GRAPH
DEFINITION:
A graph in which each edge connects two different vertices and where
no two edges connect the same pair of vertices is called a simple graph.
.

10.  no two edges connect the same pair of vertices

11.  The maximum number of edge possible in a
single graph with ‘n’ vertices
is;
nC2 = n(n-1)/2

12. Exercise Question(pg # 650) Q(1-10)
10. For each undirected graph in Exercises 3–9 that is not simple, find a set of
edges to remove to make it simple.
Qno : 03
This graph is simple because each edge
is connected with two different vertices.

13.  Qno 6;
Not a simple Graph.
We can make it simple
graph by removing only one
edge between a and c and
between b and d.

14. MULTI GRAPH
Definition:
Graphs that may
have multiple edges connecting
the same vertices are called
multigraphs.

15.  QNO : 4

16. Pseudo Graph
Definition
Graphs that may
include loops, and possibly
multiple edges connecting the
same pair of vertices or a vertex
to itself, are sometimes called
pseudographs.

17. Multiple Edges Allowed? Loop Allowed?
Simple Graph NO NO
Multi Graph YES NO
Pseudo Graph YES YES
Graph Terminology