1 Answer this question on the insert provided.
The nodes in the unfinished graph in Fig. 1 represent six components, A, B, C, D, E, F and the mains. The components are to be joined by electrical cables to the mains. Each component can be joined directly to the mains, or can be joined via other components.
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\includegraphics[alt={},max width=\textwidth]{03df7d9e-63d4-48fb-9cf3-e92003f44788-2_486_879_623_607}
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\caption{Fig. 1}
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The total number of connections that the electrician has to make is the sum of the orders of the nodes in the finished graph.
- Draw arcs representing suitable cables so that the electrician has to make as few connections as possible. Give this number.
The electrician has a junction box. This can be represented by an eighth node on the graph.
- What is the minimum number of connections which the electrician will have to make if he uses the junction box?
- The electrician has to make more connections if he uses his junction box. Why might he choose to use it anyway?
The electrician decides not to use the junction box. He measures each of the distances between pairs of nodes, and records them in a complete graph. He then constructs a minimum connector for his graph to find which nodes to connect.
- Will this result in the minimum number of connections? Justify your answer.