4. Find the Minimal Spanning Tree of the following network 35 30 N 12 18 15 39 12 16
4. Find the Minimal Spanning Tree of the following network 35 30 N 12 18 15 39 12 16
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:### Problem 4: Minimal Spanning Tree Problem
**Objective:**
Find the Minimal Spanning Tree of the following network.
**Network Diagram:**
The network is represented by a graph with six nodes (numbered 1 through 6) and weighted edges connecting these nodes. The weights of the edges are as follows:
- Node 1 to Node 2: 35
- Node 1 to Node 3: 30
- Node 2 to Node 3: 12
- Node 2 to Node 4: 18
- Node 2 to Node 6: 39
- Node 3 to Node 4: 15
- Node 4 to Node 5: 12
- Node 4 to Node 6: 16
- Node 5 to Node 6: 30
### Explanation:
In the graph provided:
- Node 1 is connected to Nodes 2 and 3 with weights 35 and 30, respectively.
- Node 2 is connected to Nodes 1, 3, 4, and 6 with weights 35, 12, 18, and 39, respectively.
- Node 3 is connected to Nodes 1, 2, and 4 with weights 30, 12, and 15, respectively.
- Node 4 is connected to Nodes 2, 3, 5, and 6 with weights 18, 15, 12, and 16, respectively.
- Node 5 is connected to Nodes 4 and 6 with weights 12 and 30, respectively.
- Node 6 is connected to Nodes 2, 4, and 5 with weights 39, 16, and 30, respectively.
To find the Minimal Spanning Tree (MST), you need to determine a subset of the edges that connects all the vertices together without any cycles and with the minimum possible total edge weight.
### Instructions for Finding Minimal Spanning Tree:
1. **Prim's Algorithm** or **Kruskal's Algorithm** can be used to find the MST of the given network.
2. You can start with any node (say Node 1) and successively add the smallest edge that connects a new node to the tree while avoiding cycles.
3. Repeat the process until all nodes are connected.
### Example Solution Approach:
1. Start with the smallest edge: Node 2 to Node
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