Problem 11. (10 points) After running BFS and DFS on many examples, most people tend to think (have the intuition that) BFS usually results in a bushier tree (higher degree nodes & longest path in the tree short) while DFS usually results in a vinelike tree (lower degree nodes & longest path in the tree longer). An extreme case is when the graph has every node connected to every other node and BFS yields a star while DFS yields a line. However, a student claims that there is a graph G and vertex A where running BFS results in a tree where every node has degree 1 or 2, but running DFS results in a tree with at least 1 node of degree 3. Either find such a graph and vertex or prove that it cannot occur