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A spanning tree is an application of a network There is another type of spanning tree called the minimum spanning tree This data structure is used in many business applications I will be discussing what a spanning tree is and what a minimum spanning tree is and how they work I will also discuss how spanning trees are used in every day business 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 There are many algorithms written on minimum spanning trees here are two of the most common Prims algorithm and Kruskals algorithm Prims 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 Prims algorithm is correct because at each stage it has built a minimum spanning tree over those vertices in the
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