The number of different spanning trees in complete graph, K4 and bipartite…

Answer: 16 for K4 and 4 for K_{2,2}.

Reason:

For a complete graph K_n, use Cayley's formula:

• Number of spanning trees = n^{n-2}.

• For K4: n = 4, so number = 4^{4-2} = 4^2 = 16.

For a complete bipartite graph K_{m,n}, use the formula:

• Number of spanning trees = m^{n-1} * n^{m-1}.

• For K_{2,2}: m = 2, n = 2, so number = 2^{1} * 2^{1} = 4.

Therefore the correct pair of counts is 16 for K4 and 4 for K_{2,2}, matching the option showing '16, 4'.