1 The arc weights for a network on a complete graph with six vertices are given in the following table.
| A | B | \(C\) | D | E | \(F\) |
| A | - | 5 | 7 | 9 | 8 | 12 |
| B | 5 | - | 4 | 6 | 5 | 10 |
| C | 7 | 4 | - | 7 | 6 | 8 |
| D | 9 | 6 | 7 | - | 5 | 10 |
| E | 8 | 5 | 6 | 5 | - | 10 |
| F | 12 | 10 | 8 | 10 | 10 | - |
Apply Prim's algorithm to the table in the Printed Answer Book. Start by crossing out the row for \(A\) and choosing an entry from the column for \(A\). Write down the arcs used in the order that they are chosen. Draw the resulting minimum spanning tree and give its total weight.