Union of subgraphs with respect to some ideals on near rings

In our work, the new concept of union in certain graphs: WI(N), API(N), ΓI(N) and PGI(N) are dealt, which depends on the case of the intersection of edges in the subgraphs in which it equals an empty set, as well as a study of the case of homomorphism, where we reached many new theorems and Results that can be generalized to other graphs or algebra graph theory.