2. (10 points) Suppose we have a connected graph G (V,E and a specified vertex S EV. Suppose we construct a depth-first search tree rooted at s, and obtain the tree T. Suppose we then run breadth-first search on G starting at s, and obtain the same tree T. Prove that G 3. (10 points) Prove by example that, in the previous problem, if the breadth-first search were started at a different vertex s'nes, and we obtained the same tree T, it does not follow that G T