THE RELATION BETWEEN PRODUCTS OF GRAPHS AND THE AUTOMORPHISM GROUPS OF GRAPHS

We show that the factorization of a graph Γ with respect to the Cartesian product (the direct product) comes from the factorization of the T-act V (Γ) and the factorization induced by it on the T-act E(Γ), where T is a subgroup of Aut(Γ), the automorphism group of Γ.