Quick questions on Minimum Spanning Trees - TCE Mathematics Applications (Tasmania)

A network usually has many spanning trees. The minimum spanning tree (MST) is the one with the smallest total edge weight. It is the cheapest way to connect everything while never forming a loop, because a loop would add cost without connecting any new vertex.

Prim's algorithm grows one connected tree from a starting vertex, but Kruskal's algorithm offers a different route to the same minimum spanning tree. Instead of growing from one point, Kruskal's sorts all the edges from cheapest to dearest and adds them one at a time, skipping any edge that would close a cycle, until $v - 1$ edges have been chosen. The two methods always reach the same total weight on a network with distinct edge weights, so you can use whichever the question suggests or use one to check the other.