Appreciate step solution.

This question explores how graph algorithms can be applied to a graph with an unknown edge weight. Graph W is shown in the following diagram. The vertices of W represent tourist attractions in a city. The weight of each edge represents the travel time, to the nearest minute, between two attractions. The route between A and F is currently being resurfaced and this has led to a variable travel time. For this reason, AF has an unknown travel time x minutes, where xe Z*. B 6 C A 5 H X 10 8 D 5 G F 10 8 11 E 3 (a) Write down a Hamiltonian cycle in W. Daniel plans to visit all the attractions, starting and finishing at A. He wants to minimize his travel time. To find a lower bound for Daniel's travel time, vertex A and its adjacent edges are first deleted. (b) (i) Use Prim's algorithm, starting at vertex B, to find the weight of the minimum spanning tree of the remaining graph. You should indicate clearly the order in which the algorithm selects each edge. [5] (ii) Hence, for the case where x