Question: 5. Minimum spanning tree and travelling salesman. Given complete weighted graph G(VE) with 6 vertices and weights given by the distance matrix D: D= 2

5. Minimum spanning tree and travelling salesman. Given complete weighted graph G(VE) with 6 vertices and weights given by the distance matrix D: D= 2 3 4 5 11 2 5 6 7 4 3 5 8 1 2 4 6 8 9 10 5 7 1 9 3 11 4 2 10 3 (a) Plot the complete graph GV.E): 2 marks (b) Find the minimum spanning tree by using Prim's algorithm? SHOW YOUR WORK, following steps of the method. 8 marks (c) Find the minimum spanning tree by using Greedy (Kruskal) algorithm? SHOW YOUR WORK 8 marks (d) Assume that a traveling salesman starts his tour from vertex 1 (and needs to return to vertex 1). Find his tour and total distance by using greedy algorithm, similar to Kruskal. HINT: beside avoiding cycles, avoid to add edge whose degree is larger than 2 in the current step. 2 marks

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