1.
| A | B | C | D | E | F | G | H |
| A | - | 9 | 8 | 13 | 17 | 11 | 12 | 10 |
| B | 9 | - | 11 | 21 | 15 | 24 | 13 | 7 |
| C | 8 | 11 | - | 20 | 23 | 17 | 17 | 15 |
| D | 13 | 21 | 20 | - | 15 | 28 | 11 | 18 |
| E | 17 | 15 | 23 | 15 | - | 31 | 23 | 30 |
| F | 11 | 24 | 17 | 28 | 31 | - | 13 | 15 |
| G | 12 | 13 | 17 | 11 | 23 | 13 | - | 23 |
| H | 10 | 7 | 15 | 18 | 30 | 15 | 23 | - |
The table represents a network that shows the time taken, in minutes, to travel by car between eight villages, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } , \mathrm { F } , \mathrm { G }\) and H .
- Use Prim's algorithm, starting at A , to find a minimum spanning tree for this network. You must list the arcs that form your tree in the order in which you select them.
- Draw your minimum spanning tree using the vertices given in Diagram 1 in the answer book and state the weight of the tree.
- State whether your minimum spanning tree is unique. Justify your answer.