1. WELCOME TO OUR
PRESENTATION
PRESENTED BY:
NAME- MD.MINHAJUL-ABEDIN ID-171-15-
1386
NAME- MD.OLIDE HASAN ID-181-15-
1791
PRESENTATION TOPIC – GRAPHS
PRESENTED TO: FARIA
NISHAT KHAN
LECTURER, DEPARTMENT OF CSE
2. CONTENT-
• Definition of Graph
• Some important points
• Types of graphs
• Walk
• Euler path & circuit
• Shortest Path Problems
3. DEFINITION OF GRAPH
A graph is a mathematical diagram which shows the relationship
between two or more sets of numbers or measurements.
Formally, a graph is a pair of sets (V,E), where V is the set of
vertices and E is the set ofset of ; edges, formed by pairs of
vertices.
It is a pair G = (V, E), where
V = V(G) = set of vertices
E = E(G) = set of edges
Example:
V = {s, u, v, w, x, y, z}
E = {(x,s), (x,v), (x,v), (x,u), (v,w), (s,v), (s,u), (s,w), (s,y), (w,y),
4. SOME IMPORTANT POINTS
• Loop and Multiple Edges
A loop is an edge whose endpoints are equal i.e., an edge joining
a vertex to it self is called a loop. We say that the graph has
multiple edges if in the graph two or more edges joining the
same pair of vertices.
5. TYPES OF GRAPH
• Simple Graph
A graph with no loops or multiple edges is called a simple graph.
We specify a simple graph by its set of vertices and set of edges,
treating the edge set as a set of unordered pairs of vertices and
write e = uv (or e = vu) for an edge e with endpoints u and v.
• Connected Graph
A graph that is in one piece is said to be connected,
whereas one which splits into several pieces is
disconnected.
6. SUBGRAPH
A graph all of whose points and lines are contained in a larger
graph.
Let G be a graph with vertex set V(G) and edge-list E(G). A
subgraph of G is a graph all of whose vertices belong to V(G) and
all of whose edges belong to E(G). For example, if G is the
connected graph below: • w, z} and E(G) = (uv, uw, vv, vw, wz,
wz} then the following graphs are
7. WALK
A walk is a sequence of vertices and edges of a graph
8. EULER PATH & CIRCUIT-
Euler Path is a path in the graph that passes each edge only
once. Euler Circut is a path in the graph that passes each edge
only once and return back to its original position. From Denition,
Euler Circuit is a subset of Euler Path
9. SHORTEST PATH PROBLEMS
• Directed weighted graph.
• Path length is sum of weights of edges on path.
• The vertex at which the path begins is the source vertex.
• The vertex at which the path ends is the destination vertex.
