3 This diagram shows a network.
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- Obtain a minimum connector for this network. Draw your minimum connector, state the order in which the arcs were chosen and give their total weight.
- Use the nearest neighbour method, starting from vertex \(A\), to find a cycle that passes through every vertex.
The network represents a cubical die, with vertices labelled \(A\) to \(H\), and faces numbered from 1 to 6 in such a way that the numbers on each pair of opposite faces add up to 7 . When two faces meet in an edge, the sum of the numbers on the two faces is recorded as the weight on that edge.
- (a) List the vertices of each of the two faces that meet in the edge \(A G\).
(b) What number is on the face \(A C E G\) ?
(c) Which face is numbered 3?