Mid Project Presentation

1. Mid Project Presentation Project Title: Four Color Theorem Group Members: • Amjad Aziz • Rizwan Hanif • Jaffar Hussain • Arif Amir • KhurramAltaf

2. Agenda • Introduction • Current Status • Demo • Future Work

3. Four Color Theorem • In mathematics, the four color theorem, or the four color map theorem, states that given any separation of a plane into contiguous regions, called a map, the regions can be colored using at most four colors so that no two adjacent regions have the same color. Two regions are called adjacent only if they share a border segment, not just a point.

4. Colored Graph

5. Assumptions(1) Adjacency Matrix Graph 2 1 5 3 4 Writing input.txt from the given Graph…

6. Assumptions(2) input.txt Adjacency matrix Converting input.txt into Adjacency Matrix …………

7. Assumptions(3) Adjacency Matrix …. Adjacency matrix Graph 2 1 5 3 4 Converting input.txt into Adjacency Matrix …………

8. Assumptions(4) • We will use only 4 colors to give distinct color to adjacent nodes. • In the previous example the graph contain the 5 nodes. We are using the Brute force attack • Possible combinations will be 45. • Combination sequence format is

9. Assumptions(5) Checking the Combination In the Adjacency Matrix

10. Running the program and the output… • Total combinations are 1024 • One valid combination. • 0 1 1 0 2 • Total valid combinations are 168 • Time taken is 17 mSec • Press any key to continue... • Say • 0Green • 1 Red • 2Yellow • 3Blue 2 1 5 3 4

11. Enter the no of Nodes:

12. Drawing nodes on graph

13. Table

14. Running Program..

15. Total count is 422=17592186044416 combinations Total valid combinations are 0 1 0 1 0 1

16. Thank you