Question

What is wrong with this? Discrete Math Use Prim's algorithm starting with vertex \( v_{0} \) 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-separat

Answer 1

The edges were added in the following order: 12-2, 2-5, 5-10, 10-13, 13-15, 15-18, 18-19, 19-20, 20-12.

Explanation:

Prim's algorithm is a method for finding the minimum spanning tree of a connected weighted graph. In this scenario, the algorithm starts at vertex 12 and systematically adds edges to construct the minimum spanning tree. The edges are selected based on their weights, with the goal of minimizing the total weight of the tree.

The first edge added is 12-2, the shortest among the available options. Subsequently, the algorithm adds edges 2-5, 5-10, 10-13, 13-15, 15-18, 18-19, and finally 19-20. This sequence ensures that at each step, the algorithm chooses the edge with the smallest weight connecting a vertex in the tree to a vertex outside the tree. The process continues until all vertices are included in the minimum spanning tree.

By following this approach, the algorithm guarantees an optimal solution, as it consistently selects the minimum-weight edges, resulting in a tree that spans all vertices with the least total weight possible. The final order of edges, 12-2, 2-5, 5-10, 10-13, 13-15, 15-18, 18-19, and 19-20, represents the path the algorithm took to achieve the minimum spanning tree.

Full Question:

Utilize Prim's calculation beginning with vertex v to discover a least crossing tree for the chart. Demonstrate the arrangement in which edges are included to create the tree. 12 20 2 10 Us 18 19 15 13 12 12 20 20 5 /Us 10 10 13 13 12 Us 20 4 10 10 18 13 comma-separated list of sets.) In what arrangement were the edges included?

Answer 2

The order in which the edges were included in the spanning tree is as follows: (v, v1), (v1, v5), (v5, v)

To discover the least traversing tree utilizing Prim's calculation, we begin with the vertex v and include the edge with the littlest weight that interfaces v to a vertex that's not as of now within the tree. We repeat this handle until all vertices are within the tree.

Within the picture, able to see that the edge with the littlest weight is (v, v_1), with weight 12. We include this edge to the tree and move on to the next step.

The following littlest edge is (v1, v5), with weight 10. We include this edge in the tree, but we must watch out not to make a cycle. The edge (v_5, v_4') also has a weight of 10, but including this edge would make a cycle between v, v_1, v_5, and v_4'. Hence, we skip this edge and move on to another step.

The following littlest edge is (v5, v6), with weight 13. We include this edge in the tree, and we presently have a spanning tree for the graph

The order in which the edges were included in the spanning tree is as follows:

(v, v1)

(v1, v5)

(v5, v6)


The complete question:

Utilize Prim's calculation beginning with vertex v to discover a least crossing tree for the chart. Demonstrate the arrangement in which edges are included to create the tree. 12 20 2 10 Us 18 19 15 13 12 12 20 20 5 /Us 10 10 13 13 12 Us 20 4 10 10 18 13 comma-separated list of sets.) In what arrangement were the edges included?

The diagram is attached below: