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Use Kruskal's algorithm to find a minimum spanning tree for the following graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.) 12 20 5 4 10 V5 V3 18 19 8 15 13 7.

Use Kruskal's algorithm to find a minimum spanning tree for the following graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.) 12 20 5 4 10 V5 V3 18 19 8 15 13 7.

Advanced Engineering Mathematics
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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### Kruskal's Algorithm for Minimum Spanning Tree Use Kruskal's algorithm to find a minimum spanning tree for the following graph. Indicate the order in which edges are added to form the tree. **Steps to follow:** 1. **Sort all edges in the graph by their weight in non-decreasing order.** 2. **Starting from the smallest edge, add the edge to the spanning tree if it doesn't form a cycle with the edges already included in the tree. Repeat until there are \(|V| - 1\) edges in the tree, where \(|V|\) is the number of vertices.** **Graph Description:** The graph consists of 8 vertices labeled from \(v_0\) to \(v_7\). The edges between these vertices have the following weights: - \(v_0 \to v_5\) with weight 4 - \(v_5 \to v_6\) with weight 8 - \(v_0 \to v_1\) with weight 12 - \(v_1 \to v_3\) with weight 7 - \(v_1 \to v_2\) with weight 20 - \(v_2 \to v_3\) with weight 2 - \(v_3 \to v_4\) with weight 15 - \(v_4 \to v_5\) with weight 10 - \(v_4 \to v_6\) with weight 13 - \(v_4 \to v_7\) with weight 5 - \(v_7 \to v_3\) with weight 18 - \(v_7 \to v_6\) with weight 19 Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets of edges.) ### Graphical Representation The graph shows vertices connected with lines, and each line has a number indicating the weight of the edge. The edges can be visualized connecting different pairs of vertices (nodes) with specified weights. ### Objective Find the minimum spanning tree by systematically adding edges with the smallest weights while ensuring no cycles are formed, until all vertices are connected. **Example Response:** ``` {v2, v3}, {v0, v5}, {v1, v
Transcribed Image Text:### Kruskal's Algorithm for Minimum Spanning Tree Use Kruskal's algorithm to find a minimum spanning tree for the following graph. Indicate the order in which edges are added to form the tree. **Steps to follow:** 1. **Sort all edges in the graph by their weight in non-decreasing order.** 2. **Starting from the smallest edge, add the edge to the spanning tree if it doesn't form a cycle with the edges already included in the tree. Repeat until there are \(|V| - 1\) edges in the tree, where \(|V|\) is the number of vertices.** **Graph Description:** The graph consists of 8 vertices labeled from \(v_0\) to \(v_7\). The edges between these vertices have the following weights: - \(v_0 \to v_5\) with weight 4 - \(v_5 \to v_6\) with weight 8 - \(v_0 \to v_1\) with weight 12 - \(v_1 \to v_3\) with weight 7 - \(v_1 \to v_2\) with weight 20 - \(v_2 \to v_3\) with weight 2 - \(v_3 \to v_4\) with weight 15 - \(v_4 \to v_5\) with weight 10 - \(v_4 \to v_6\) with weight 13 - \(v_4 \to v_7\) with weight 5 - \(v_7 \to v_3\) with weight 18 - \(v_7 \to v_6\) with weight 19 Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets of edges.) ### Graphical Representation The graph shows vertices connected with lines, and each line has a number indicating the weight of the edge. The edges can be visualized connecting different pairs of vertices (nodes) with specified weights. ### Objective Find the minimum spanning tree by systematically adding edges with the smallest weights while ensuring no cycles are formed, until all vertices are connected. **Example Response:** ``` {v2, v3}, {v0, v5}, {v1, v
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