Graph theory is the study of points and lines, and concepts like vertices and edges. It has many applications, including map coloring, Google Maps, and football games. Graph theory can be used to color maps with the minimum number of colors without any adjacent regions sharing the same color. It is also used in Google Maps for functions like estimating travel times and showing traffic conditions. In football, a match can be represented as a network with players as vertices and passes as edges, allowing analysis of things like which team has a more balanced network.

2. GRAPH THEORY
IN
REAL LIFE
APPLICATION

3. Presented By
Ms. R. Umadevi
Assistant Professot of Mathematics,
Bon Secours College For Women,
Thanjavur

4. Graph theory :
 It is study of points & lines . It is concepts of vertices,
nodes or points which are connected to the edges , arc ,
lines .
Example:

5. COMPLETE GRAPH

6. MAP COLOURING:
Rules:

7. CHROMATC NUMBERS:
 Minimum number of colour used in the graph
Example:

8. Applications of graph colouring
used:
 CPU register
 Football games
 Fish tank problem
 Radio network
 Map colouring
 Cell phone network
 Traffic signals

9. •DISCUSS:
Map colouring
Google map
Football

10. Graph theory in map colouring:

11. Map coloured with four colour

12. Graph theory used in Google
maps:

13. GRAPH THEORY IN GOOGLE
MAP

14. GOOGLE MAP

17.  Its also used in maps & GPS services
 It also say how much time to take travel, speed
limits, traffic lights, road traffic condition , etc.

18. Graph theory in Football:
*Facts of football
 A team consists of exactly
 1 goal keeper,
 3-5 defender,
 3-5 mid fielders and
 1-3 strikers

19.  We are going to discuss about the graphical representation
of 2010 FIFA WORLD CUP between the country
Netherland and Spain.

20. Graphical representation of the
game:
 We consider the football match to be analogous to a
directed network.
 The players of the team are represented as the vertices.
 The passes exchanged between players are the arcs, the
direction of the arcs will be in according to the direction
of ball pass.

22. The network between
Netherlands and Spain:

23. Degree of centrality
 Degree of centrality is the number of incident with a
vertex.
 This concept can be extended to a player by
counting the number of passes he is involved in the
game.

25. Observation:
 The spain player have higer degrees.
 There are lot of passes between all the different players ,
hence they have as balance network.

26. Netherland team:

27. Spain team:

28. COMPARISION:
NETHERLAND SPAIN

29. Observation:
 The Spain team players makes extremely large no of
passes comparing to Dutch team.
 Thus Spain team win the match is calculated by graph
theory.

30. Result:
 Using graph theory in the football match, we can
determine
 how the team win ?,
 How many players passes how many ball?,
 Using this we can find the balanced network.

31. Conclusion :
 Graph theory used in many fields , it will give the
approximate solutions to the problem.
 Through this graph theory we are able solve many
problems which are involved in many field.

32. THANK YOU