(Discrete Math) ### Prim's Algorithm and Minimum Spanning TreeTo find a minimum spanning tree for a weighted undirected graph using Prim's algorithm, you can follow these steps:1. **Start from the selected vertex (v0)**: - In this case, vertex $ v_0 $ is the starting point.2. **Grow the spanning tree**: - Always choose the smallest weight edge that connects a vertex in the growing spanning tree to a vertex outside of it but is connected to it.The provided graph and algorithm details are as follows:#### Graph BreakdownVertices: $ v_0, v_1, v_2, v_3, v_4, v_5, v_6, v_7 $Edges with Weights:- $ v_0 - v_5 $ with weight 4- $ v_0 - v_1 $ with weight 12- $ v_1 - v_3 $ with weight 7- $ v_1 - v_2 $ with weight 20- $ v_2 - v_3 $ with weight 2- $ v_3 - v_4 $ with weight 15- $ v_3 - v_7 $ with weight 18- $ v_4 - v_5 $ with weight 10- $ v_4 - v_7 $ with weight 15- $ v_6 - v_7 $ with weight 13- $ v_5 - v_6 $ with weight 8#### Steps to Find the Minimum Spanning Tree (MST):1. Start with vertex $ v_0 $.2. Select the edge with the smallest weight connected to it (in this case, $ (v_0, v_5) $ with weight 4).3. Now consider vertices $ v_0, v_5 $.4. Choose the edge $ (v_5, v_6) $ with weight 8.5. Now consider vertices $ v_0, v_5, v_6 $.6. Select the edge $ (v_4, v_5) $ with weight 10.7. Now consider vertices $ v_0, v_4, v_5, v_6 $.8. Select the edge \( (v

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Use Prim's algorithm starting with vertex v, to find a minimum spanning tree for the graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.) 12 7. 20 10 2 V5 15 18 19 13 4-

Use Prim's algorithm starting with vertex v, to find a minimum spanning tree for the graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.) 12 7. 20 10 2 V5 15 18 19 13 4-

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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Question

(Discrete Math)

### Prim's Algorithm and Minimum Spanning Tree
To find a minimum spanning tree for a weighted undirected graph using Prim's algorithm, you can follow these steps:

1. **Start from the selected vertex (v0)**:
- In this case, vertex $ v_0 $ is the starting point.

2. **Grow the spanning tree**:
- Always choose the smallest weight edge that connects a vertex in the growing spanning tree to a vertex outside of it but is connected to it.

The provided graph and algorithm details are as follows:

#### Graph Breakdown
Vertices: $ v_0, v_1, v_2, v_3, v_4, v_5, v_6, v_7 $

Edges with Weights:
- $ v_0 - v_5 $ with weight 4
- $ v_0 - v_1 $ with weight 12
- $ v_1 - v_3 $ with weight 7
- $ v_1 - v_2 $ with weight 20
- $ v_2 - v_3 $ with weight 2
- $ v_3 - v_4 $ with weight 15
- $ v_3 - v_7 $ with weight 18
- $ v_4 - v_5 $ with weight 10
- $ v_4 - v_7 $ with weight 15
- $ v_6 - v_7 $ with weight 13
- $ v_5 - v_6 $ with weight 8

#### Steps to Find the Minimum Spanning Tree (MST):
1. Start with vertex $ v_0 $.
2. Select the edge with the smallest weight connected to it (in this case, $ (v_0, v_5) $ with weight 4).
3. Now consider vertices $ v_0, v_5 $.
4. Choose the edge $ (v_5, v_6) $ with weight 8.
5. Now consider vertices $ v_0, v_5, v_6 $.
6. Select the edge $ (v_4, v_5) $ with weight 10.
7. Now consider vertices $ v_0, v_4, v_5, v_6 $.
8. Select the edge \( (v

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