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In mathematical graph theory, the rooted product of a graph G and a rooted graph H is defined as follows: take |V| copies of H, and for every vertex v i {\displaystyle v_{i}} of G, identify v i {\displaystyle v_{i}} with the root node of the i-th copy of H.
More formally, assuming that V = {g1,..., gn}, V = {h1,..., hm} and that the root node of H is h 1 {\displaystyle h_{1}} , define
where
and
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