3.
| A | B | C | D | E | F | G | H | J |
| A | - | 3 | 8 | 5 | - | - | - | - | - |
| B | 3 | - | 4 | - | - | - | - | - | - |
| C | 8 | 4 | - | - | 9 | 4 | - | - | - |
| D | 5 | - | - | - | - | 7 | 4 | 9 | - |
| E | - | - | 9 | - | - | 4 | - | - | 7 |
| F | - | - | 4 | 7 | 4 | - | - | 8 | 13 |
| G | - | - | - | 4 | - | - | - | 4 | - |
| H | - | - | - | 9 | - | 8 | 4 | - | 7 |
| J | - | - | - | - | 7 | 13 | - | 7 | - |
The table above shows the lengths, in metres, of the paths between nine vertices, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } , \mathrm { F }\), G, H and J.
- Use Prim's algorithm, starting at A , to find a minimum spanning tree for this table of distances. You must clearly state the order in which you select the edges and state its weight. Draw your minimum spanning tree using the vertices in the answer book.
- State whether your minimum spanning tree is unique. Justify your answer.
- Use Dijkstra's algorithm to find the length of the shortest path from A to J.