  In this work we have re-investigated two different kinds of texture zero
ansatz of the low energy neutrino mass matrix in view of the
Dark-Large-Mixing-Angle (DLMA) solution of the solar neutrino problem which can
arise in the presence of non-standard interactions. In particular we revisit
the cases of (i) one zero mass matrices when the lowest neutrino mass is zero
and (ii) one zero texture with a vanishing minor. In our study we find that for
most of the cases, the texture zero conditions which are allowed for the LMA
solution, are also allowed for the DLMA solution. However, we found two
textures belonging to the case of one zero texture with a vanishing minor where
LMA solution does not give a viable solution whereas DLMA solution does. We
analyze all the possible texture zero cases belonging to these two kinds of
texture zero structures in detail and present correlations between different
parameters. We also present the predictions for the effective neutrino mass
governing neutrino-less double beta decay for the allowed textures.
