  Many pulsating low-mass white-dwarf stars have been detected in the last
years in the field of our Galaxy. Given that some of them exhibit multiperiodic
variation of brightness, it is possible to probe their interiors through
asteroseismology. We present a detailed asteroseismological study of all the
known low-mass variable white dwarf stars based on a complete set of fully
evolutionary models representative of low-mass He-core white dwarf stars. We
employed adiabatic radial and nonradial pulsation periods for low-mass white
dwarf models with stellar masses ranging from $0.1554$ to $0.4352\ M_{\odot}$,
that were derived by simulating the nonconservative evolution of a binary
system consisting of an initially $1 M_{\odot}$ ZAMS star and a $1.4 M_{\odot}$
neutron star companion. We estimated the mean period spacing for the stars
under study and then we used the comparison between the observed period spacing
with the average of the computed period spacings for our grid of models to
constrain the stellar mass. We also employed the individual observed periods of
every known pulsating low-mass white dwarf star, to search for a representative
seismological model. We found that even though the stars under analysis exhibit
few periods and the period fits show multiplicity of solutions, it is possible
to find seismological models whose mass and effective temperature are in
agreement with the values given by spectroscopy, for most of the cases. In the
two cases where we could extract the period spacing from the set of observed
periods, this method led to values of the stellar masses substantially larger
than expected for this type of stars. The results presented in this work show
in the one hand, the need for further photometric searches, and on the other
hand, some improvements of the theoretical models, in order to place the
asteroseismological results on a firmer ground.
