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
Related questions
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2abc661b-c0c9-4b79-9347-0fc323cf483e%2F2887e4c9-b991-4d2e-96f1-1e0d65f6dec8%2F2u93l8fa_processed.png&w=3840&q=75)
Transcribed Image Text:### 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
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)