Answer
The minimum spanning tree includes the four edges BD, AC, AD, and DE.
The total weight of the minimum spanning tree is 875.
Work Step by Step
We can use Kruskal's Algorithm to find the minimum spanning tree for the weighted graph.
First, we choose the smallest weight, which is 170. We add the edge BD to the spanning tree.
The next smallest weight is 190, so we add edge AC to the spanning tree.
The next smallest weight is 205, so we add edge AD to the spanning tree.
The next smallest weight is 210. However, this edge would make a circuit so we do not add the edge AB to the spanning tree.
The next smallest weight is 307. However, this edge would make a circuit so we do not add the edge BC to the spanning tree.
The next smallest weight is 310, so we add edge DE to the spanning tree.
Now we have created a spanning tree that includes all the vertices, is connected, and does not have any circuits.
The minimum spanning tree includes the four edges BD, AC, AD, and DE.
We can find the total weight of the minimum spanning tree.
total weight = 170 + 190 + 205 + 310
total weight = 875
The total weight of the minimum spanning tree is 875.
