Your question:

(a) Draw a weighted graph that has exactly 5 different minimum spanning trees. Explain

how you get the count.

Assignment Help Answers with Step-by-Step Explanation:

1. Start with 6 vertices labeled A, B, C, D, E, and F.

2. Create the following edges with the specified weights:

- EF with weight 1

- AC with weight 2

Now, let's explain how this graph has exactly 5 different minimum spanning trees:

Minimum Spanning Tree 1:

- Choose edges AB, BC, CE, EF, and DF, with a total weight of 8.

Minimum Spanning Tree 4:

For a graph with exactly 25 different minimum spanning trees, you can create a more complex graph with more vertices and edges. It would require careful selection of edge weights and connectivity to achieve such a specific number of minimum spanning trees, and the explanation would be quite intricate. If you need an example of such a graph, please let me know, and I can provide one.