  The thermally pulsing phase on the asymptotic giant branch (TP-AGB) is the
last nuclear burning phase experienced by most of low and intermediate mass
stars. During this phase, the outer chemical stratification above the C/O core
of the emerging white dwarf is built up. The chemical structure resulting from
progenitor evolution strongly impacts the whole pulsation spectrum exhibited by
ZZ Ceti stars, which are pulsating C/O core white dwarfs located on an narrow
instability strip at T eff \sim 12000 K. Several physical processes occurring
during progenitor evolution strongly affect the chemical structure of these
stars, being those found during the TP-AGB phase ones of the most relevant for
the pulsational properties of ZZ Ceti stars. We present a study of the impact
of the chemical structure built up during the TP-AGB evolution on the stellar
parameters inferred from asteroseismological fits of ZZ Ceti stars. Our
analysis is based on a set of carbon-oxygen core white dwarf models with masses
from 0.534 to 0.6463M_{\odot} derived from full evolutionary computations from
the ZAMS to the ZZ Ceti domain. We compute evolutionary sequences that
experience different number of thermal pulses. We find that the occurrence or
not of thermal pulses during AGB evolution implies an average deviation in the
astero- seimological effective temperature of ZZ Ceti stars of at most 8% and
of the order of < 5% in the stellar mass. For the mass of the hydrogen
envelope, however, we find deviations up to 2 orders of magnitude in the case
of cool ZZ Ceti stars. For hot and intermediate temperature ZZ Ceti stars shows
no differences in the hydrogen envelope mass in most cases. Our results show
that, in general, the impact of the occurrence or not of thermal pulses in the
progenitor stars is not negligible and must be taken into account in
asteroseismological studies of ZZ Ceti stars.
