6.
| \(A\) | B | C | D | \(E\) | \(F\) |
| A | - | 7 | 3 | - | 8 | 11 |
| B | 7 | - | 4 | 2 | - | 7 |
| C | 3 | 4 | - | 5 | 9 | - |
| D | - | 2 | 5 | - | 6 | 3 |
| E | 8 | - | 9 | 6 | - | - |
| \(F\) | 11 | 7 | - | 3 | - | - |
The matrix represents a network of roads between six villages \(A , B , C , D , E\) and \(F\). The value in each cell represents the distance, in km, along these roads.
- Show this information on the diagram in the answer book.
(2) - Use Kruskal's algorithm to determine the minimum spanning tree. State the order in which you include the arcs and the length of the minimum spanning tree. Draw the minimum spanning tree.
(5) - Starting at \(D\), use Prim's algorithm on the matrix given in the answer book to find the minimum spanning tree. State the order in which you include the arcs.
(3)