Real life application

Real Life Application of Graph Theory

1. GRAPH THEORY IN REAL LIFE APPLICATION  

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

3. 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:

4. COMPLETE GRAPH

5. MAP COLOURING: Rules:

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

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

8. DISCUSS: Map colouring Google map Football

9. Graph theory in map colouring:

10. Map coloured with four colour

11. Graph theory used in Google maps:

12. GRAPH THEORY IN GOOGLE MAP

13. GOOGLE MAP

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

15. 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

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

17. 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 .

18. The network between Netherlands and Spain:

19. 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.

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

21. Netherland team:

22. Spain team:

23. COMPARISION: NETHERLAND SPAIN

24. 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.

25. 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.

26. 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.

27. THANK YOU