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 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 Tis 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.)