Quivers supporting twisted Calabi-Yau algebras

We consider graded twisted Calabi-Yau algebras of dimension 3 which are derivation-quotient the form A=kQ/I, where Q is a quiver and I an ideal relations coming from taking partial derivatives superpotential on Q. define type (M,P,d) such algebra A, M incidence matrix quiver, P permutation giving action Nakayama automorphism A vertices d degree superpotential. study question what possible types can occur under additional assumption that has polynomial growth. In particular, we able to give nearly complete answer this when at most vertices.