1.
| \(\mathbf { A }\) | \(\mathbf { B }\) | \(\mathbf { C }\) | \(\mathbf { D }\) | \(\mathbf { E }\) | \(\mathbf { F }\) |
| \(\mathbf { A }\) | - | 135 | 180 | 70 | 95 | 225 |
| \(\mathbf { B }\) | 135 | - | 215 | 125 | 205 | 240 |
| \(\mathbf { C }\) | 180 | 215 | - | 150 | 165 | 155 |
| \(\mathbf { D }\) | 70 | 125 | 150 | - | 100 | 195 |
| \(\mathbf { E }\) | 95 | 205 | 165 | 100 | - | 215 |
| \(\mathbf { F }\) | 225 | 240 | 155 | 195 | 215 | - |
The table shows the lengths, in km, of potential rail routes between six towns, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E }\) and F .
- Use Prim's algorithm, starting from A , to find a minimum spanning tree for this table. You must list the arcs that form your tree in the order that they are selected.
- Draw your tree using the vertices given in Diagram 1 in the answer book.
- State the total weight of your tree.