Final answer:
The statement is true; a graph can have many different spanning trees. The exact number depends on the graph's structure and can be quite large for even small graphs.
Step-by-step explanation:
The statement, "A graph can have many spanning trees," is true. Spanning trees are subsets of a graph that include all the vertices covered by the original graph with the minimum number of edges required to maintain the graph connected. The number of possible spanning trees can vary greatly, depending on the structure of the original graph. For example, a complete graph with n vertices has n^(n-2) different possible spanning trees, according to Cayley's formula. This shows that even a small graph can have a large number of different spanning trees.