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Assume a graph is having 10 vertices and 20 edges. In Kruskal’s minimum spanning tree method, 5 edges are rejected. How many edges are not considered during execution of algorithm on the given graph?a.10b.6c.4d.5

Question

Assume a graph is having 10 vertices and 20 edges. In Kruskal’s minimum spanning tree method, 5 edges are rejected. How many edges are not considered during execution of algorithm on the given graph?a.10b.6c.4d.5

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Solution

In Kruskal's algorithm, we start by sorting all the edges from low weight to high. After sorting, we iterate through the sorted edges and add it to the minimum spanning tree. If adding the edge created a cycle, then we reject it.

Given that a graph has 10 vertices and 20 edges, and 5 edges are rejected in Kruskal’s minimum spanning tree method, we can calculate the number of edges not considered during the execution of the algorithm as follows:

  1. We know that a tree with n vertices has (n-1) edges. So, a minimum spanning tree with 10 vertices will have (10-1) = 9 edges.

  2. If 5 edges are rejected, that means 9 + 5 = 14 edges were considered during the execution of the algorithm.

  3. The total number of edges in the graph is 20. So, the number of edges not considered during the execution of the algorithm is 20 - 14 = 6.

So, the answer is (b) 6.

This problem has been solved

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