numbers = dict()
N = 7
for n in range(1,N+1):
    # P_n
    G = graphs.PathGraph(n)
    numbers[G.canonical_label().copy(immutable=True)] = 2^(n-1)

    # C_n
    # Theorem 2.2
    if n > 2:
        G = graphs.CycleGraph(n)
        if is_even(n):
            numbers[G.canonical_label().copy(immutable=True)] = 2^(n//2)
        else:
            numbers[G.canonical_label().copy(immutable=True)] = 2*(2^((n+1)//2)//3) + 1
    
def statistic(G):
    global numbers
    if not G.is_connected():
        return
    G = G.canonical_label().copy(immutable=True)
    if G in numbers:
        return numbers[G]
    n = G.num_verts()
    if G.is_clique():
        return n
    # Theorem 2.7
    if G.is_triconnected() and G.diameter() == 2:
        return n