  We have presented the role of the Coulomb interaction ($U$) and the magnetic
field ($\vec{B}$) on the ground state properties of the quasi-one dimensional
graphite ribbon structures at half-filling. Mean field Hartree-Fock
Approximation is used to study the systems. To understand the boundary effects
in graphite structures, we have compared the results of these systems with
those of the square lattice ribbon structures. Studying the density of states,
the Drude weight and the charge gap, we have drawn the $U-B$ phase diagrams for
the zigzag and the armchair graphite ribbons.
