Irreducible Graphs Modulo n

Recently, it has found a connection between graph theory and the theory of factorizations.  This work focused particularly in the case of τ_n-factorizations and graph theory.  In other words, in the τ_n-factorization which I can multiply only elements in the same equivalence class, the difference is divisible by n  or equivalently its difference belongs to the principal ideal generated by n .  We present some examples, properties and patterns of τ_n-factorizations τ_n-product for 2,3,4 and 5 modulos. Also, I present one characterization of irreducible graph modulo.