- (a) Draw the complete graph \(K _ { 5 }\).
(b) Demonstrate that no planar drawing is possible for \(K _ { 5 }\).
(c) Draw the complete graph \(K _ { 3,3 }\).
(d) Demonstrate that no planar drawing is possible for \(K _ { 3,3 }\). - A project consists of 11 activities, some of which are dependent on others having been completed. The following precedence table summarises the relevant information.
| Activity | Depends on | Duration (hours) |
| A | - | 5 |
| B | A | 4 |
| C | A | 2 |
| D | B, C | 11 |
| E | C | 4 |
| \(F\) | D | 3 |
| \(G\) | D | 8 |
| \(H\) | D, E | 2 |
| I | \(F\) | 1 |
| J | \(F , G , H\) | 7 |
| \(K\) | \(I , J\) | 2 |
Draw an activity network for the project. You should number the nodes and use as few dummies as possible.
(7 marks)