The composition G = G_1[G_2] of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph with point vertex V_1×V_2 and u = (u_1, u_2) adjacent with v = (v_1, v_2) whenever [u_1 adj v_1] or [u_1 = v_1 and u_2 adj v_2]. It is also called the graph lexicographic product.

graph lexicographic product | graph product