Rooted product of graphs

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 v i {displaystyle v_{i}} of G, identify v i {displaystyle v_{i}} with the root node of the i-th copy of H. 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 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(G) = {g1, ..., gn}, V(H) = {h1, ..., hm} and that the root node of H is h 1 {displaystyle h_{1}} , define