  It was shown recently, that normalized relations between the moment of
inertia (I), the quadrupole moment (Q) and the tidal deformability (Love
number) exist and for slowly-rotating neutron stars they are almost independent
of the equation of state (EOS). We extend the computation of the I-Q relation
to models rotating up to the mass-shedding limit and show that the universality
of the relations is lost. With increasing rotation rate, the normalized I-Q
relation departs significantly from its slow-rotation limit deviating up to 40%
for neutron stars and up to 75% for strange stars. The deviation is also EOS
dependent and for a broad set of hadronic and strange matter EOS the spread due
to rotation is comparable to the spread due to the EOS, if one considers
sequences with fixed rotational frequency. Still, for a restricted sample of
modern realistic EOS one can parameterize the deviations from universality as a
function of rotation only. The previously proposed I-Love-Q relations should
thus be used with care, because they lose their universality in astrophysical
situations involving compact objects rotating faster than a few hundred Hz.
