  We present our study on atomic, electronic, magnetic and phonon properties of
one dimensional honeycomb structure of molybdenum disulfide (MoS$_2$) using
first-principles plane wave method. Calculated phonon frequencies of bare
armchair nanoribbon reveal the fourth acoustic branch and indicate the
stability. Force constant and in-plane stiffness calculated in the harmonic
elastic deformation range signify that the MoS$_2$ nanoribbons are stiff quasi
one dimensional structures, but not as strong as graphene and BN nanoribbons.
Bare MoS$_2$ armchair nanoribbons are nonmagnetic, direct band gap
semiconductors. Bare zigzag MoS$_2$ nanoribbons become half-metallic as a
result of the (2x1) reconstruction of edge atoms and are semiconductor for
minority spins, but metallic for the majority spins. Their magnetic moments and
spin-polarizations at the Fermi level are reduced as a result of the
passivation of edge atoms by hydrogen. The functionalization of MoS$_2$
nanoribbons by adatom adsorption and vacancy defect creation are also studied.
The nonmagnetic armchair nanoribbons attain net magnetic moment depending on
where the foreign atoms are adsorbed and what kind of vacancy defect is
created. The magnetization of zigzag nanoribbons due to the edge states is
suppressed in the presence of vacancy defects.
