2. A graph G consists of a finite set of ordered pairs, called
edges E, of certain entities called vertices V. Edges are
also called as arcs or links. Vertices are also called as
nodes or points.
A graph is a set of vertices and edges. A vertex may
represent a state or a condition while the edge may
represent a relation between two vertices.
Directed Graphs or DIGRAPHS make reference
to edges which are directed (i.e.) edges which
are ordered pairs of vertices.
A graph whose definition makes reference to
unordered pairs of vertices as edges is known
as an undirected graph
3. APPLICATIONS OF GRAPH
Amazon use graphs to make suggestions for
Graph is use in solving Travelling Salesman Problem
(TSP) Branch and bound algorithms
o Logistics of delivering goods
o Sport Tournament
o Drilling holes in circuit boards
o Programming space telescopes like Hubble
The seven bridges of Konigsberg
Social Networks (Facebook) use graph for finding
Solving Traffic Control Problems
4. GRAPH APPLICATIONS IN
TRAFFIC CONTROL PROBLEMS
The Traffic control problem at a four leg intersection,
with five streams and the corresponding compatibility
graph as shown below:
5. The traffic control problem is to minimize the
waiting time of the public transportation while
maintaining the individual traffic flow optimally.
Vehicles approaching an intersection prepare
themselves to perform a certain maneuver i.e.
to drive through, turn left, or turn right at an
The resulting compatibility graph of the
intersection and its connectivity is used to study
the most efficient route or the traffic control
system to direct the traffic flow to its maximum
capacity using the minimum number of edges
or the minimum number of vertices.
As the edges of the edge connectivity represents the
flow of traffic at an intersection, the waiting time of
the traffic participants can be minimized by
controlling the edges of the edge connectivity .
The traffic sensors can be placed on each edge in a
cut-set of G determined by its edge connectivity as
well as on each vertex of G determined by its vertex
connectivity. These sensors will provide complete
traffic information for the control system.