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Find the minimum spanning tree for the of the graph. 35 55 B 18 35 70 40. H D 3 40 G 21 20 E 50

Find the minimum spanning tree for the of the graph. 35 55 B 18 35 70 40. H D 3 40 G 21 20 E 50

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Finding the Minimum Spanning Tree for a Graph In this educational exercise, you are required to find the minimum spanning tree of a given graph. The graph is composed of 9 vertices connected by weighted edges. Each vertex is indicated by a letter (A-J), and the weights (distances) between the vertices are represented as numerical values along the edges connecting them. #### Graph Description The vertices in the graph are labeled as follows: - A - B - C - D - E - F - G - H - J The weighted edges between the vertices are as follows: - A to B: 55 - A to J: 35 - B to C: 35 - B to J: 8 - C to D: 3 - C to H: 70 - C to G: 40 - D to E: 21 - E to F: 50 - F to G: 20 ### Steps to Find the Minimum Spanning Tree To find the minimum spanning tree (MST) of this graph, you can use algorithms such as Prim's or Kruskal's algorithm. Below is a brief outline of the process using Kruskal's algorithm: 1. **Sort all edges**: Begin by sorting all the edges in the graph in ascending order based on their weights. 2. **Select the smallest edge**: Start with the smallest edge and add it to the MST, ensuring you do not form a cycle. 3. **Repeat**: Continue to add the next smallest edge to the MST, again ensuring no cycles are formed, until spanning the entire graph. 4. **Check**: Verify that all vertices are included in the MST. By applying either Prim's or Kruskal's algorithm, you can systematically determine the minimum spanning tree for this graph, ensuring the total weight (sum of the edges in the tree) is minimized. ### Visual Representation The graph provided in the image shows a network of vertices and edges with varying weights. For better understanding and accurate calculation, you can draw the graph on paper or use graph visualization software to implement the MST finding algorithm.
Transcribed Image Text:### Finding the Minimum Spanning Tree for a Graph In this educational exercise, you are required to find the minimum spanning tree of a given graph. The graph is composed of 9 vertices connected by weighted edges. Each vertex is indicated by a letter (A-J), and the weights (distances) between the vertices are represented as numerical values along the edges connecting them. #### Graph Description The vertices in the graph are labeled as follows: - A - B - C - D - E - F - G - H - J The weighted edges between the vertices are as follows: - A to B: 55 - A to J: 35 - B to C: 35 - B to J: 8 - C to D: 3 - C to H: 70 - C to G: 40 - D to E: 21 - E to F: 50 - F to G: 20 ### Steps to Find the Minimum Spanning Tree To find the minimum spanning tree (MST) of this graph, you can use algorithms such as Prim's or Kruskal's algorithm. Below is a brief outline of the process using Kruskal's algorithm: 1. **Sort all edges**: Begin by sorting all the edges in the graph in ascending order based on their weights. 2. **Select the smallest edge**: Start with the smallest edge and add it to the MST, ensuring you do not form a cycle. 3. **Repeat**: Continue to add the next smallest edge to the MST, again ensuring no cycles are formed, until spanning the entire graph. 4. **Check**: Verify that all vertices are included in the MST. By applying either Prim's or Kruskal's algorithm, you can systematically determine the minimum spanning tree for this graph, ensuring the total weight (sum of the edges in the tree) is minimized. ### Visual Representation The graph provided in the image shows a network of vertices and edges with varying weights. For better understanding and accurate calculation, you can draw the graph on paper or use graph visualization software to implement the MST finding algorithm.
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