3 The following network shows the lengths, in miles, of roads connecting nine villages, \(A , B , \ldots , I\).
\includegraphics[max width=\textwidth, alt={}, center]{1258a6d3-558a-46dc-a916-d71f71b175ff-06_810_501_445_388}
\includegraphics[max width=\textwidth, alt={}, center]{1258a6d3-558a-46dc-a916-d71f71b175ff-06_812_499_443_1135}

1. 1. Use Prim's algorithm starting from \(A\), showing the order in which you select the edges, to find a minimum spanning tree for the network.
   2. State the length of your minimum spanning tree.
   3. Draw your minimum spanning tree.
2. Prim's algorithm from different starting points produces the same minimum spanning tree for this network. State the final edge that would complete the minimum spanning tree using Prim's algorithm:
   1. starting from \(D\);
   2. starting from \(H\).