  Let $A$ be a finite dimensional representation-finite algebra over an
algebraically closed field. The aim of this work is to generalize the results
proven in CGS. Precisely, we determine which vertices of $Q_A$ are sufficient
to be considered in order to compute the nilpotency index of the radical of the
module category of a monomial algebra and a toupie algebra $A$, when the
Auslander-Reiten quiver is not necessarily a component with length.
