  A mathematical approach is adopted for optimizing the number of total device
elements required for obtaining high effective quantized resistances in
graphene-based quantum Hall array devices. This work explores an analytical
extension to the use of star-mesh transformations such that fractal-like, or
recursive, device designs can yield high enough resistances (like 1 E{\Omega},
arguably the highest resistance with meaningful applicability) while still
being feasible to build with modern fabrication techniques. Epitaxial graphene
elements are tested, whose quantized Hall resistance at the nu=2 plateau (R_H =
12906.4 {\Omega}) becomes the building block for larger effective, quantized
resistances. It is demonstrated that, mathematically, one would not need more
than 200 elements to achieve the highest pertinent resistances
