  Electron transport and quantum conductance through an armchair graphene and
its oxidized graphene- containing form were investigated by the density
functional theory (DFT) method and the implementation of the non-equilibrium
Green function (NEGF) approach. The computed $I-V_b$(current as a function of
bias voltage) characteristic of the studied systems showed the tunneling
phenomenon in bias and gate voltages considered. Along with the transport
properties, electronic properties including density of states (DOS) were
calculated in the studied systems. A close examination of the results showed
that the $I-V_b$ curve for graphene behaved $I\propto V_be^{\lambda V_b}$ like
at some bias voltages, while for the oxidized graphene-containing form, its
trend was the same as that of a Voltage Dependent Resistor (VDR-VARiable
resISTOR), $I\propto V_b^\beta$, at the whole range of the applied bias.
