Every F-heavy edge deleted is not in the minimum spanning tree by the cycle property.

Prim's purpose is to find a minimum spanning tree for a graph.

Each isolated vertex is a separate component of the minimum spanning forest.

If each edge has a distinct weight then there will be only one, unique minimum spanning tree.

Research has also considered parallel algorithms for the minimum spanning tree problem.

They were used to achieve the best complexity to date for finding a minimum spanning tree.

Depending on what the graph looks like, there may be more than one minimum spanning tree.

It can be very simple to make an algorithm that will discover a minimum spanning tree:

This is similar to the minimum spanning tree problem which concerns undirected graphs.

It is also used for implementing Kruskal's algorithm to find the minimum spanning tree of a graph.