Question: 11. Suppose that G= (V, E) is a weighted, connected, undirected graph, and assume that all edge-weights are distinct. Let T be a MST of

11. Suppose that G= (V, E) is a weighted, connected, undirected

11. Suppose that G= (V, E) is a weighted, connected, undirected graph, and assume that all edge-weights are distinct. Let T be a MST of G. Consider the following claim: "For every v EV, the minimum-weight edge incident to v in G must be in T." (a) Show how this claim follows from the correctness of Prim's algorithm. You may assume that Prim's algorithm is correct. (b) Show how this claim follows from the correctness of Kruskal's algorithm. You may assume that Kruskal's algorithm is correct. 11. Suppose that G= (V, E) is a weighted, connected, undirected graph, and assume that all edge-weights are distinct. Let T be a MST of G. Consider the following claim: "For every v EV, the minimum-weight edge incident to v in G must be in T." (a) Show how this claim follows from the correctness of Prim's algorithm. You may assume that Prim's algorithm is correct. (b) Show how this claim follows from the correctness of Kruskal's algorithm. You may assume that Kruskal's algorithm is correct

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