Context : 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 .

Aims : 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 .

Methods : Our analysis is based on a set of carbon-oxygen core white dwarf models with masses from 0.534 to 0.6463 M _ { \sun } derived from full evolutionary computations from the ZAMS to the ZZ Ceti domain .
We compute evolutionary sequences that experience different number of thermal pulses .

Results : We find that the occurrence or not of thermal pulses during AGB evolution implies an average deviation in the asteroseimological effective temperature of ZZ Ceti stars of at most 8 % and of the order of \lesssim 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 .

Conclusions : 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 .