Final answer:
No, it is not possible to use the same minimum spanning tree when the edge weights are squared.
Step-by-step explanation:
The answer to this question is B) No, it is not possible to use the same minimum spanning tree when the edge weights are squared.
The minimum spanning tree is a tree that connects all the vertices of a graph with the minimum total edge weight. Squaring the edge weights will change the relative weights of the edges, therefore changing the minimum spanning tree as well.
For example, consider a graph with three vertices A, B, and C, and edges AB, AC, and BC. If the original edge weights are 2, 3, and 4 respectively, the minimum spanning tree would connect vertices A and C with an edge weight of 3. However, if we square the edge weights to 4, 9, and 16, the minimum spanning tree would connect vertices A and B with an edge weight of 4.
However, if we square the weights, A-B becomes weight 1 and B-C becomes weight 4, which does not change the MST for this particular graph. But, if there was another path from A to C via another node with an original edge weight less than 4, squaring the weights could lead to a different minimum spanning tree. Therefore, whether the MST stays the same after squaring the weights depends on the specific weights and structure of the original graph.