4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{acc09687-11a3-4392-af17-3d4d331d5ab4-05_501_493_196_529}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{figure}
Figure 3 shows the graph \(K _ { 4 }\).
- State the features of the graph that identify it as \(K _ { 4 }\).
- In \(K _ { 4 }\), the Hamiltonian cycles \(A B C D A , B C D A B , C D A B C\) and \(D A B C D\) are usually regarded as being the same cycle. Find the number of distinct Hamiltonian cycles in
- \(\quad K _ { 4 }\),
- \(K _ { 5 }\),
- \(K _ { 10 }\).
- In a weighted network, 8 possible routes must be placed in ascending order according to their lengths. The routes have the following lengths in kilometres:
$$\begin{array} { l l l l l l l l }
27 & 25 & 29 & 32 & 19 & 24 & 17 & 26
\end{array}$$
Use a quick sort to obtain the sorted list, giving the state of the list after each comparison and indicating the pivot elements used.