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A minimum spanning tree (MST) is not necessarily unique. While there is only one MST with the minimum total weight for certain graphs, when there are multiple edges with the same weight, there can be more than one valid MST. In such cases, different spanning trees with the same weight may be possible. For example, in a graph with parallel edges of equal weight, there can be multiple ways to select edges while still maintaining the minimum total weight. The characteristics of an MST ensure that it has the least total weight, contains exactly V−1V-1 V − 1 edges, and connects all vertices without forming cycles. However, its uniqueness can be compromised in cases of weight ties. Therefore, it’s incorrect to assume that an MST is always unique. Why Other Options Are Incorrect:
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