Question: 3. Let G (V, E) be a simple undirected connected graph with n vertices. The BFS and the DFS traversals generate rooted and ordered traversal

3. Let G (V, E) be a simple undirected connected graph with n vertices. The BFS and the DFS traversals generate rooted and ordered traversal trees. The structure and the height of these trees may depend on the starting vertex and the order among the vertices when applying the traversals procedures. The height of a rooted tree is the distance in edges from the root to the furthest leaf. For example, the height of a tree with one vertex is 0, the height of a path tree for which the root is one of its end vertices is n -1, and the height of a star tree for which the center vertex is the root is 1. For each one of the following cases determine the possible structure of the traversal tree and its possible maximum and minimum height. You may assume that n is large enough. Graph Traversal structure(s) max. height min height Complete DFS Complete BFS DFS Path Path BFS Cycle DFS Cycle Star Star BFS DFS BFS a. Illiustrate all possible structures of the traversals trees generated by DFS on the wheel graph Wn. b. IIlistrate all possible structures of the traversals trees generated by BFS on the wheel graph W

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