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We demonstrate one of the basic building elements of graphene electronics, logic inverter, based on graphene-on-boron nitride material system. The inverter is composed of two adjacent graphene-channel field-effect transistors (GFETs). The impacts of hexagonal boron nitride, a new supporting substrate material, on major device performance metrics of GFET such as small-signal transconductance g m and effective carrier mobility μeff are explored. The prototype of logic inverter is demonstrated on a single sheet of CVD-assembled monolayer graphene based on the unique ambipolar conduction behavior of the 2-D nanoscale carbon system.