Chapter 14 - Graph Theory - 14.4 Trees - Exercise Set 14.4 - Page 933: 50

Using Kruskal's Algorithm, we can find the minimum spanning tree. First we find the edge with the smallest weight and add this to the spanning tree. Then we find the next smallest weight, and as long as the edge does not make a circuit, we add the edge to the spanning tree. We continue adding edges like this until all the vertices from the original graph have been included in the spanning tree.

The minimum spanning tree is the spanning tree which has the smallest total weight. Using Kruskal's Algorithm, we can find the minimum spanning tree. First we find the edge with the smallest weight and add this to the spanning tree. Then we find the next smallest weight, and as long as the edge does not make a circuit, we add the edge to the spanning tree. We continue adding edges like this until all the vertices from the original graph have been included in the spanning tree. If the original graph has n vertices, then the spanning tree has n vertices and n-1 edges. The spanning tree is connected and it has no circuits.