A complete bipartite graph is a graph where there are two sets of vertices, and every vertex in one set is connected to every vertex in the other set. The number of vertices in one set is denoted as 'm' and the number of vertices in the other set is denoted as 'n'.
In this problem, we are given that m = 4 and n = 4. The total number of vertices in the graph is m+n = 4+4 = 8.
The number of spanning trees of a complete bipartite graph with 'm' and 'n' vertices can be calculated using the formula: (m^(n-2)) * (n^(m-2))
In this case, the number of spanning trees of the graph is: (4^(4-2)) * (4^(4-2)) = 4^2 * 4^2 = 16 * 16 = 256
So, the number of spanning trees of the complete bipartite graph with 4 and 4 vertices is 256.
It is important to note that this formula works only for complete bipartite graph and not for any other type of graph.