Rings of Graphs

We construct all possible rings taking graphs as elements, the union or sum of graphs as the binary operation of the group and graph product as the second operation. Furthermore we show that every ring formed with union operation is isomorphic to some ring with sum operation. In every case, we give an homomorphism from the ring to the integers polynomial. (This is an extended abstract of Campanelli, Nicolas, Martín Eduardo Frías Armenta and Jose L. Martinez-Morales, Ring of graphs, Submited to boletin de la sociedad mexicana de matemáticas.)