2. An electronics company makes a product that consists of components \(A , B , C , D , E\) and \(F\). The table shows which components must be connected together to make the product work. The components are all placed on a circuit board and connected by wires, which are not allowed to cross.
| Component | Must be connected to |
| \(A\) | \(B , D , E , F\) |
| \(B\) | \(C , D , E\) |
| \(C\) | \(D , E\) |
| \(D\) | \(E\) |
| \(E\) | \(F\) |
| \(F\) | \(B\) |
- On the diagram in the answer book draw straight lines to show which components need to be connected.
(1) - Starting with the Hamiltonian cycle \(A B C D E F A\), use the planarity algorithm to determine whether it is possible to build this product on a circuit board.
(4)