Question

by the end of this task you should understand how to determine relevant edges in a spanning tree. follow along with your teacher as you determine the minimum weight spanning tree for the graph below.

Explanation:

Step1: Select minimum - weight edge

Start with the edge with the minimum weight. The edge EG has weight 1.

Step2: Select next minimum - weight edge

Among the remaining non - cycle forming edges, the edge CF has weight 2 and edge GH has weight 2. We can choose one of them. Let's choose CF first.

Step3: Select another non - cycle edge

Now, choose GH as it is a non - cycle forming edge with minimum weight among the remaining ones.

Step4: Select more non - cycle edges

Next, we can choose edge AF with weight 4. Then edge CD with weight 7. Then edge DH with weight 4.

Step5: Calculate total weight

Sum up the weights of the selected edges: $1 + 2+2 + 4+7 + 4=20$.

Answer:

The minimum weight of the spanning tree is 20.