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I haven't checked it thoroughly yet, so please let me know if there are any issues.

def rooted_product_of_graphs(G, H):
    V = [(gi, hj) for gi in G.nodes() for hj in H.nodes()]
    E = []
    h0 = next(iter(H.nodes()))
    for (gi, gk) in G.edges():
            E.append(((gi, h0), (gk, h0)))

    for hj, hk in H.edges():
        for gi in G.nodes():
            E.append(((gi, hj), (gi, hk)))

    rooted_product = E
    return rooted_product
import networkx as nx
G = nx.Graph()
G.add_nodes_from([1, 2, 3, 4, 5])
G.add_edges_from([(1, 2), (2, 3),(3,4),(4,5),(5,2)])

H = nx.Graph()
H.add_nodes_from(['a', 'b','c','d'])
H.add_edges_from([('a', 'b'),('b', 'c'),('b', 'd')])

print(rooted_product_of_graphs(G, H))

I haven't checked it thoroughly yet, so please let me know if there are any issues.

def rooted_product_of_graphs(G, H):
    V = [(gi, hj) for gi in G.nodes() for hj in H.nodes()]
    E = []
    h0 = next(iter(H.nodes()))
    for (gi, gk) in G.edges():
            E.append(((gi, h0), (gk, h0)))

    for hj, hk in H.edges():
        for gi in G.nodes():
            E.append(((gi, hj), (gi, hk)))

    rooted_product = E
    return rooted_product
import networkx as nx
G = nx.Graph()
G.add_nodes_from([1, 2, 3, 4, 5])
G.add_edges_from([(1, 2), (2, 3),(3,4),(4,5),(5,2)])

H = nx.Graph()
H.add_nodes_from(['a', 'b','c','d'])
H.add_edges_from([('a', 'b'),('b', 'c'),('b', 'd')])

print(rooted_product_of_graphs(G, H))

I haven't checked it thoroughly yet, so please let me know if there are any issues.

def rooted_product_of_graphs(G, H):
    V = [(gi, hj) for gi in G.nodes() for hj in H.nodes()]
    E = []
    h0 = next(iter(H.nodes()))
    for (gi, gk) in G.edges():
            E.append(((gi, h0), (gk, h0)))

    for hj, hk in H.edges():
        for gi in G.nodes():
            E.append(((gi, hj), (gi, hk)))

    rooted_product = return E
    return rooted_product
import networkx as nx
G = nx.Graph()
G.add_nodes_from([1, 2, 3, 4, 5])
G.add_edges_from([(1, 2), (2, 3),(3,4),(4,5),(5,2)])

H = nx.Graph()
H.add_nodes_from(['a', 'b','c','d'])
H.add_edges_from([('a', 'b'),('b', 'c'),('b', 'd')])

print(rooted_product_of_graphs(G, H))

output: [((1, 'a'), (2, 'a')), ((2, 'a'), (3, 'a')), ((2, 'a'), (5, 'a')), ((3, 'a'), (4, 'a')), ((4, 'a'), (5, 'a')), ((1, 'a'), (1, 'b')), ((2, 'a'), (2, 'b')), ((3, 'a'), (3, 'b')), ((4, 'a'), (4, 'b')), ((5, 'a'), (5, 'b')), ((1, 'b'), (1, 'c')), ((2, 'b'), (2, 'c')), ((3, 'b'), (3, 'c')), ((4, 'b'), (4, 'c')), ((5, 'b'), (5, 'c')), ((1, 'b'), (1, 'd')), ((2, 'b'), (2, 'd')), ((3, 'b'), (3, 'd')), ((4, 'b'), (4, 'd')), ((5, 'b'), (5, 'd'))]

I haven't checked it thoroughly yet, so please let me know if there are any issues.

def rooted_product_of_graphs(G, H):
    V = [(gi, hj) for gi in G.nodes() for hj in H.nodes()]
    E = []
    h0 = next(iter(H.nodes()))
    for (gi, gk) in G.edges():
            E.append(((gi, h0), (gk, h0)))

    for hj, hk in H.edges():
        for gi in G.nodes():
            E.append(((gi, hj), (gi, hk)))

    return E
import networkx as nx
G = nx.Graph()
G.add_nodes_from([1, 2, 3, 4, 5])
G.add_edges_from([(1, 2), (2, 3),(3,4),(4,5),(5,2)])

H = nx.Graph()
H.add_nodes_from(['a', 'b','c','d'])
H.add_edges_from([('a', 'b'),('b', 'c'),('b', 'd')])

print(rooted_product_of_graphs(G, H))

output: [((1, 'a'), (2, 'a')), ((2, 'a'), (3, 'a')), ((2, 'a'), (5, 'a')), ((3, 'a'), (4, 'a')), ((4, 'a'), (5, 'a')), ((1, 'a'), (1, 'b')), ((2, 'a'), (2, 'b')), ((3, 'a'), (3, 'b')), ((4, 'a'), (4, 'b')), ((5, 'a'), (5, 'b')), ((1, 'b'), (1, 'c')), ((2, 'b'), (2, 'c')), ((3, 'b'), (3, 'c')), ((4, 'b'), (4, 'c')), ((5, 'b'), (5, 'c')), ((1, 'b'), (1, 'd')), ((2, 'b'), (2, 'd')), ((3, 'b'), (3, 'd')), ((4, 'b'), (4, 'd')), ((5, 'b'), (5, 'd'))]