Spanning trees

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)]