QUESTION 3 20 MARKS a) Either draw a full m-ary tree with 13 leaves and height 2 where m is a positive integer or show that no such tree exists. 2 marks) i. b) The word 'SALUTE' is resulted from in-order traversal of a rooted binary tree. Draw the tree with height of 2 that can represent the above traversal. (2% marks) Using tree draw in ) find the word resulted from the pre-order traversal. (2% marks) c) Draw two spanning trees from the graph in Figure 3. (3 marks) ii. 6 Figure 3 d) Data Communication company has offices A, B, C, D, E, F, G, and H. Table 1 shows the cost, in Ringgit Malaysia (RM), of transmitting a piece of information from one of the offices to another along all existing direct links. Table 1 TO A B D E F G H From A 8 10 5 B 8 4 4 4 4 4 3 3 D 3 1 6 2 E 4 1 3 F 10 4 3 6 G 2 3 3 H 5 4 3 i. ii. Construct a network using vertices A to H to represent the information in Table 1. (3 marks) A piece of information has to be passed from office A to all the other offices, either directly or by being passed on from office to office. Use Kruskal's algorithm to find the minimum total cost of passing the information to all the offices. (6 marks) 111. Draw a network that produces the minimum total cost in (ii). (1 mark)