Problem 5: [4 marks]| Add the following elements to an initially empty B-tree. The order of the B-tree is 8. Draw the resulting B-tree. 33453886532 1121732552367 153911 1948 Problem 6: [4 marks] Show the resulting B-tree by removing the following elements from the resultant tree created by Problem 5. 11217325523 1948 Problem 7: Vertices (nodes): 1,2,3,4,5,6,7 Edges (connections): (1, 2), (1, 4), (2, 3), (2, 4), (3, 7), (4, 7). (4, 6), (5, 6), (5, 7), (6, 7) (a) Draw the undirected graph using the information on the vertices and edges above. [2 marks] (b) Is the resulting graph complete? Is it connected? [2 marks] () Indicate all the cycles in the undirected graph. [2 marks] (d) Draw a spanning tree for the resulting undirected graph. [2 marks] (e) Draw the directed graph using the information on the vertices and edges above. [2 marks] (f) Is the resulting directed graph complete? Is it connected? [2 marks] (g) Indicate all the cycles in the directed graph. [2 marks] (h) Draw a spanning tree for the resulting directed graph. [2 marks] Problem 8: [4 mark] Using the following directed graph, perform the breadth-first traversal starting from C. Assume we always choose the letter closest to the beginning of the alphabet first. Show each step showing the content of the queue and iterator. Problem 9: [4 marks] Repeat Problem 2 for the depth-first traversal using a stack and iterator. Problem 10: [6 marks] Perform Dijkstra's algorithm on the following graph to find the shortest path between @) to (7). Show each step of executing the algorithm. 2