Please provide working and explanation

a) Given the following undirected graph: 10 6 6 B 3 3 2 Start A 3 2 2 11 E H 11 Represent the graph as: (1) Adjacency matrix (ii) Adjacency list (ill) Incidence matrix (1,0 mark) (1.0 mark) (1.0 mark) b) Given the above-undirected graph, use Dijkstra's shortest-path algorithm to compute the shortest path from A to all network nodes. (i) Show how the algorithm works by computing a table like the one discussed in class. (3.0 marks) (1) Show all the paths from node 0 to all other network nodes. (1.0 mark) c) Consider the following search problem, represented as a graph. Each node is label by a capital letter and the value of a heuristic function is shown in maroon, Each edge is labelled by the cost to traverse that edge. The start state is 'D' and the only goal state is 'G' (1) Is the heuristics specified in the problem above permissible? Justify your answer. If the heuristics is permissible, proceed to answer part c(ii), if the heuristics is not permissible, correct it with a sensible value of your choice and proceed to answer part c(it). (1.0 mark) (ii) Perform the A* search to find the shortest path from node D to node G. (2.0 marks) Start 30 33 3 27 27 B 24 10 9 0 8 F 10 D E 10 20 16 Numbers in maroon are the heuristics for the respective nodes. Numbers in black are the weight (estimated costs.)