3 The following network shows the lengths, in miles, of roads connecting ten villages, \(A , B , C , \ldots , J\).
\includegraphics[max width=\textwidth, alt={}, center]{77c4efd4-a905-48f3-a6f7-36b0e47dbc6d-06_899_1458_397_285}
- Use Kruskal's algorithm, showing the order in which you select the edges, to find a minimum spanning tree for the network.
- Find the length of your minimum spanning tree.
- Draw your minimum spanning tree.
- Prim's algorithm from different starting points produces the same minimum spanning tree. State the final edge that would be added to complete the minimum spanning tree if the starting point were:
- \(A\);
- \(F\).