Arithmetic Q

Question 1 Consider the following represent G. pic 1. Give the adjacency matrix and adjacency list of the graph G. (5 marks) adjacency matrix pic adjacency list a b c d e f b d a c e b e f a e b c d f c e 2. Give the incidence matrix and incidence list of the graph G. (5 marks) pic incidence matrix pic incidence list 1 2 3 4 5 6 a b a d b c b e c e c e 7 8 d e e f Question 2 Consider the graph I. kickoff at the vertex a and resolving ties by the vertex alphabetical coif traverse the graph by breadth-first-search (BFS) and construct the corresponding BFS tree. (5 marks) pic The order is a b e g f c d h II. Starting at the vertex a and resolving ties by the vertex alphabetical order traverse the graph by depth-first-search (DFS) and construct the corresponding BFS tree. (5 marks) pic The order is a b f e g c d h Question 3 Consider the following graph G.The label of an edge is the personify of the edge. 1. Using Prims algorithm, draw a nominal spanning tree (M ST) of the graph Also write down the change of the priority queue ill-treat by step and the order in which the vertices are selected. Is the MST drawn unique? (i. e. , is it the one and only MST for the graph? ) 7 marks Not unique pic 2. Using Kruskals algorithm, draw a minimum spanning tree (MST) of the graph G. Write down the order in which the edges are selected. Is the MST drawn unique? (i. e. , is it the one and only MST for the graph? ) (5 marks)Not unique pic 3. Referring to the same graph above, find the shortest paths from the vertex a to all other vertices in the graph G using Dijkstras algorithm. Show the changes of the priority queue step by step and give the order in which edges are selected. (8 marks) pic Order in which edges are selected a-e, e-f, a-b, f-g, b-c, g-h, c-d the shortest paths from the vertex a to all other vertices a. b 4 a. c 10 a. d17 a. e1 a. f3 a. g8 a. h 16 N. B. There may be more than than one solution. You only need to give one of the solutions.