This document presents a summary of minimum spanning trees by a group called DIODE. It defines a minimum spanning tree as a spanning tree that connects all vertices of a graph with the smallest possible total edge weight. It describes Prim's and Kruskal's algorithms for finding minimum spanning trees and provides example diagrams to illustrate the concepts. The document was presented by seven students to provide an overview of minimum spanning trees.

1. Welcome

2. Presentation By
DIODE
Presentation Title
Minimun Spanning Tree
► presented by
 KM Abdullah Al Muhit (183-15-11931)
 Injamam UL Haque Apu (183-15-11975)
 MD Zahid Hossain (183-15-11932)
 Sheikh Shakkafi Rahman (183-15-11838)
 Tarekul Islam (183-15-12057)
 Dip Adhikary (183-15-1247)
 Abdullah Al mamun (183-15-11852)
 Sowrab Roy (183-15-11824)

3. What is spanning tree ?
A graph, which contains all vertices with minimum number
edges in which there is no cycle
Diagram:
Graph Spanning Tree
A B
D C
A
D
B
C
A
D
B
C

4. What is minimum spanning tree?
A minimum spanning tree, in a connected weighted
is a spanning tree that has the smallest possible sum of
weights of its edges.
Diagram:
A B
C D
A
D
B
C
A
C
B
D
1
5
3 2 4
1
2
3 3
1
4
Graph minimum spanning
tree
Not a minimum spanning
tree

5. Types of minimum spanning -
1.Prim’s Algorithm
2.Kruskal’s Algorithm

6. 1.Prim’s Algorithm-
B D
A C
10
5 4
11
5
4
8
12
Diagram

7. B D
A C
10
5 4
11
5 1.No loop
2.No parallel edges
Condition for minimum spanning tree.

8. A B C D
A
B
C
0 5 10
5 0 4 11
10 4 0 5
0
∞√
√
√
√
√
√
Total Weight = 5+4+5
= 14
D 11 5∞
B D
A C
5 4 5
Diagram for minimum spanning tree

9. Kruskal’s Algorithm-
B D
A C
2
2 1
5
3
9
8
12

10. B D
A C
2
2 1
5
3
Condition for minimum spanning tree
1.No loop
2.No parallel edges

11. Edegs BC AB AC CD BD
Weight 1 2 2 3 5
B D
A C
2 1 3
Total weight = 2+1+3
= 6
√ √ × √ ×
Diagram for Minimum Spnning Tree

12. Thank you