  We employ an effective-field theory with correlations in order to study the
phase diagram and ground-state magnetizations of a selectively diluted Ising
antiferromagnet on triangular and honeycomb lattices. Dilution of different
sublattices with generally unequal probabilities results in a rather intricate
phase diagram in the sublattice dilution parameters space. In the case of the
frustrated triangular lattice antiferromagnet the selective dilution affects
the degree of frustration which can lead to some peculiar phenomena, such as
reentrant behavior of long-range order or unsaturated sublattice magnetizations
at zero temperature. The selectively diluted Ising antiferromagnet on the
honeycomb lattice is obtained as a special case when one sublattice of the
triangular lattice is completely removed by dilution.
