3 The diagram shows 10 bus stops, \(A , B , C , \ldots , J\), in Geneva. The number on each edge represents the distance, in kilometres, between adjacent bus stops.
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The city council is to connect these bus stops to a computer system which will display waiting times for buses at each of the 10 stops. Cabling is to be laid between some of the bus stops.
- Use Kruskal's algorithm, showing the order in which you select the edges, to find a minimum spanning tree for the 10 bus stops.
- State the minimum length of cabling needed.
- Draw your minimum spanning tree.
- If Prim's algorithm, starting from \(A\), had been used to find the minimum spanning tree, state which edge would have been the final edge to complete the minimum spanning tree.