1. Kruskal Algorithm KRUSKAL(V,E,W) A ← Φ For each vertex vЄG[v] Do MAKESET[v] sort E into nondecreasing order of weight w Do if FINDSET [u]≠FINDSET[v] A ← A U {(U,V)} UNION(U,V) Return (A)

2. 8 8 b c d 2 4 9 a i 14 7 11 e 3 3 10 5 f h g Given: G is a connected undirected weighted graph 6 1

3. First sort the edges according to nondecreasing order of their weight

4. 8 8 b c d 2 4 9 a i 14 7 11 e 3 3 10 5 f h g 6 1 (h,g) - weight 1 (c,f) - weight 7 ( c,i) - weight 2 (b,c) - weight 8 (i,h) - weight 3 (c,d) - weight 8 ( i,g) - weight 3 (d,e) - weight 9 (a,b) - weight 4 (e,f) -weight 10 (a,h) - weight 5 (d,f) - weight 11 (g,f) - weight 6 (b,h) weight 14

5. (h,g): Select b c d a i e f h g 1

6. (c,i): Select b c d 2 a i e f h g 1

7. Select (i,h): b c d 2 a i e 3 f h g 1

8. Reject (i,g): b c d 2 a i e 3 3 f h g 1

9. Select (a,b): b c d 4 2 a i e 3 f h g 1

10. Select (a,h): b c d 2 4 a i e 5 3 f h g 1

11. (g,f): Select b c d 4 2 a i e 3 5 f h g 6 1

12. Reject (c,f): b c d 2 4 a i 7 e 3 5 f h g 1 6

13. Select (c,d): 8 b c d 2 4 a i e 3 5 f h g 1 6

14. Reject (b,c): 8 8 b c d 4 2 a i e 3 5 f h g 1 6

15. Select (d,e): 8 b c d 4 2 9 a i e 3 5 f h g 1 6

16. Reject (e,f): 8 b c d 4 2 9 a i e 3 5 10 f h g 1 6

17. Reject (d,f): 8 b c d 4 2 9 a i e 11 3 5 f h g 1 6

18. Reject (b,h): 8 b c d 4 2 9 a i 14 e 3 5 f h g 1 6

19. Minimum Spanning Tree 8 b c d 4 2 9 a i e 3 5 f h g 1 6 Total weight(MST)=1+2+3+4+5+6+8+9=38