AMS 301.3 (Fall, 2009)Estie ArkinHomework Set # 5Due in class on Monday, October 19, 2009.Recommended Reading: Tucker, 3.1, 3.2Do Problems:Problem A: LetTbe a balanced 5-ary tree with 81 nodes.(a). How many internal nodes doesThave?(b). How many edges does the treeThave?(c). What is the height ofT?16, 26(a) — Section 3.1Problem B: (a). Determine the DFS tree ofK3,3.(b). Determine the BFS tree ofK3,3.problem C: True or False? If true, give a short proof. If false, give a counterexample:(a). For any connected graphG, all internal nodes of the BFS tree onGhave the same number of children.(b). For any connected graphG, the DFS tree onGand the BFS tree onGhave the same number of edges.Homework Set # 6Due in class on Monday, October 26, 2009.Recommended Reading: 3.3 (read the introduction on page 113, and then the section “Approximate TravelingSalesperson Tour Construction”, pages 117-120), 4.2, 4.1. Read also the handouts on the web about Dijkstra’salgorithm and the TSP tour construction.Do Problems:Problem A: Consider the following graph.ABCDEF234561