Question: 3. (25 points) We have a connected graph G (V,E) and a specific vertex u E V. Suppose we compute a depth-first search tree rooted

3. (25 points) We have a connected graph G (V,E) and

3. (25 points) We have a connected graph G (V,E) and a specific vertex u E V. Suppose we compute a depth-first search tree rooted at u, and obtain a tree T that includes in all the nodes in G. Suppose we then compute a breath-first search tree rooted at u, and it turns out that we obtain the same tree, T. Prove that G -T. (In other words, if T is both a depth-first search tree and a breath-first search tree rooted at u, then cannot contain any edges that do not belong to T.)

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