A spanning tree of a graph is just a subgraph that contains all the vertices and is a tree. A graph may have many spanning trees for instance the complete graph on four vertices has sixteen spanning trees.

A minimum spanning tree is a spanning tree in which the total weight of the lines is guaranteed to be the minimum of all possible trees in the graph. The weight of a tree is just the sum of weights of its edges, because different trees have different lengths you run in the problem of how to find the minimum length spanning tree. The problem can be solved by using an algorithm for the minimum spanning tree.

In conclusion we have seen what a spanning tree is and what a minimum spanning tree is. These two types of trees are important to networking. You can see how important spanning trees are to every day business.

Prim's algorithm for the minimum spanning tree problem follows the strategy of beginning with a small tree and growing it until it includes all vertices in the given graph. Initially the tree contains just an arbitrary starting node. At each stage a vertex not yet in the tree but closest to some vertex that is in the tree is found. This closest vertex is added to the tree. Finding the vertex allows you to improve your knowledge of the distance of the remaining vertices in the tree. A set 'done' contains the vertices in the tree. Prim's algorithm is correct because at each stage it has built a minimum spanning tree over those vertices in the set 'done' which eventually contain all the vertices.

orithms written on minimum spanning trees, here are two of the most common Prim's

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Approximate Word count = 677
Approximate Pages = 3 (250 words per page double spaced)