  Using the connection with the Frobenius manifold structure, we study the
matrix model description of minimal Liouville gravity (MLG) based on the
Douglas string equation. Our goal is to find an exact discrete formulation of
the (q,p) MLG model that intrinsically contains information about the conformal
selection rules. We discuss how to modify the Frobenius manifold structure
appropriately for this purposes. We propose a modification of the construction
for Lee-Yang series involving the $A_{p-1}$ algebra instead of the previously
used $A_1$ algebra. With the new prescription, we calculate correlators on the
sphere up to four points and find full agreement with the continuous approach
without using resonance transformations.
