Your task is to construct an undirected graph that has exactly x different spanning trees.
The graph should have the nodes 1,2,\dots,n, with the number of nodes n at most 40. The graph may not have two identical edges, and each edge should connect two different nodes.
In a file spanning.py, implement the function create_edges that constructs the desired graph. The function should return the graph as a list of edges. The number of nodes n is the largest node number that occurs on the edge list.
For example, the list [(1, 2), (2, 3), (1, 3)] means a graph with n=3 nodes and an edge for every pair of two nodes. This graph has three spanning trees, because any set of two edges is a spanning tree.
You may construct any graph with the specified properties. The function will be tested with the parameter values x=1,2,\dots,42. If a desired graph cannot be constructed, the function should return None.
def create_edges(x):
# TODO
if __name__ == "__main__":
print(create_edges(1)) # esim. [(1, 2), (2, 3)]
print(create_edges(2)) # None
print(create_edges(3)) # esim. [(1, 2), (1, 3), (2, 3)]