Making a function work for higher cases of iteration

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For constructing the Generalized Sierpinski graph as described in this paper, I wrote the following code:

def Sier(g,k,m):
for i in range(1,k):
    h = Graph()
    for j in range(0, m):
        perm = {u: (j, u) for u in g}
        gg = g.relabel(perm=perm, inplace=False)
        h.add_edges(gg.edges())
        n1 = [((a, b), (b, a)) for (a, b) in h]
        n2 =[((a,a),(a,a)) for (a,b) in h]
        x=set(n1)-set(n2)
        h.add_edges(list(x))
    g=h
return h

The parameters of the function Sier are g :graph, k :the k-th iterate of Sierpinski construction, m :the order of the graph g. The code works fine only for k=2. When I put k=3, I do not get the expected output of the graph. How do I modify the code to get the desired output for any value of k? Thanks beforehand.