Solution

The correct answer is A, C, D, B

Key Points

To arrange the given simple graphs based on the number of spanning trees they have, let's understand the properties of each graph:

• A. K3 (Complete Graph with 3 nodes):
  • A complete graph with 3 nodes has 3 spanning trees.
• B. K4 (Complete Graph with 4 nodes):
  • A complete graph with 4 nodes has 16 spanning trees.
• C. K2,2 (Complete bipartite graph with 2 nodes in each partition):
  • A complete bipartite graph K2,2 has 4 spanning trees.
• D. C5 (Cycle graph with 5 nodes):
  • A cycle graph with 5 nodes has 5 spanning trees.

Based on the above information, we can arrange the graphs in ascending order of the number of spanning trees they have:

1. A. K3 (3 spanning trees)
2. C. K2,2 (4 spanning trees)
3. D. C5 (5 spanning trees)
4. B. K4 (16 spanning trees)

So, the correct order is: A, C, D, B