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

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

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