  The effects of anisotropic nearest-neighbor (NN) and isotropic
next-nearest-neighbor (NNN) hopping integrals on the magnetic subband structure
of an electron on a triangular lattice are studied within the tight-binding
approximation. A generalized Harper equation that includes both the NN and the
NNN hopping terms is first derived. Then, the effects of anisotropic NN hopping
integrals are examined and the results are compared in detail with those of an
existing literature [Phys. Rev. B {\bf 56}, 3787 (1997)]. It is found that the
hopping anisotropy generically leads to the occurrence of band broadening and
gap closing. The effects of isotropic NNN hopping integrals are next examined,
and it is found that introducing the NNN hopping integral changes considerably
the magnetic subband structure; band broadening, gap closing, gap reopening,
and band crossing occur depending on the strength of the isotropic NNN hopping
integral. Symmetries of the magnetic subband structures with and without both
the hopping anisotropy and the isotropic NNN hopping integrals are also
discussed.
