  In a recent paper [8], it is proved that the genus two free energy of an
arbitrary semisimple Frobenius manifold can be represented as a sum of
contributions associated with dual graphs of certain stable algebraic curves of
genus two plus the so called genus two G-function, and for a certain class of
Frobenius manifolds it is conjectured that the associated genus two G-function
vanishes. In this paper, we prove this conjecture for the Frobenius manifolds
associated with simple singularities of type A.
