3.
| A | B | C | D | E | F | G |
| A | - | 15 | 19 | - | 22 | 24 | - |
| B | 15 | - | - | 8 | 13 | - | - |
| C | 19 | - | - | 12 | - | 16 | - |
| D | - | 8 | 12 | - | 10 | - | 18 |
| E | 22 | 13 | - | 10 | - | 15 | 16 |
| F | 24 | - | 16 | - | 15 | - | 17 |
| G | - | - | - | 18 | 16 | 17 | - |
The table shows the lengths, in km, of a network of roads between seven villages, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } , \mathrm { F }\) and G.
- Complete the drawing of the network in Diagram 1 of the answer book by adding the necessary arcs from vertex D together with their weights.
- Use Kruskal's algorithm to find a minimum spanning tree for the network. You should list the arcs in the order that you consider them. In each case, state whether you are adding the arc to your minimum spanning tree.
- Draw the minimum spanning tree using the vertices provided in Diagram 2 in the answer book.
- State the weight of the minimum spanning tree.