  We calculate the optical conductivity of LiV$_{2}$O$_{5}$ and
NaV$_{2}$O$_{5}$ using exact numerical diagonalization of a quarter-filled
extended Hubbard model on a system of coupled ladders. In particular,
electronic correlations are treated exactly, and a quantitative agreement
between calculated and experimentally observed optical conductivity of these
two vanadium oxides is presented. Furthermore, it is found that
LiV$_{2}$O$_{5}$ differs from NaV$_{2}$O$_{5}$ not only in the charge ordering
pattern but also in the nature of the inter-ladder coupling: In contrast to
LiV$_{2}$O$_{5}$, in NaV$_{2}$O$_{5}$ neighboring ladders are coupled by a
strong Coulomb repulsion, and not by inter-ladder hopping.
