4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4ad45e8f-f50a-4125-866b-a6951f85600f-5_661_1525_292_269}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
\section*{[The total weight of the network is 1436 m ]}
- Explain the term valency.
Figure 3 models a system of underground pipes. The number on each arc represents the length, in metres, of that pipe.
Pressure readings indicate that there is a leak in the system and an electronic device is to be used to inspect the system to locate the leak. The device will start and finish at A and travel along each pipe at least once. The length of this inspection route needs to be minimised.
- Use the route inspection algorithm to find the pipes that will need to be traversed twice. You should make your method and working clear.
- Find the length of the inspection route.
Pipe HI is now found to be blocked; it is sealed and will not be replaced. An inspection route is now required that excludes pipe HI . The length of the inspection route must be minimised.
- Find the length of the minimum inspection route excluding HI. Justify your answer.
- Given that the device may now start at any vertex and finish at any vertex, find a minimum inspection route, excluding HI.