In mathematical graph theory, the rooted product of a graph G and a rooted graph H is defined as follows: take |V(G)| copies of H, and for every vertex of G, identify with the root node of the i-th copy of H. More formally, assuming that V(G) = {g1, ..., gn}, V(H) = {h1, ..., hm} and that the root node of H is , define where and If G is also rooted at g1, one can view the product itself as rooted, at (g1, h1). The rooted product is a subgraph of the cartesian product of the same two graphs.