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
@article{arxiv.2309.15813,
title = {Fractal-like star-mesh transformations using graphene quantum Hall arrays},
author = {Dominick S. Scaletta and Swapnil M. Mhatre and Ngoc Thanh Mai Tran and Cheng-Hsueh Yang and Heather M. Hill and Yanfei Yang and Linli Meng and Alireza R. Panna and Shamith U. Payagala and Randolph E. Elmquist and Dean G. Jarrett and David B. Newell and Albert F. Rigosi},
journal= {arXiv preprint arXiv:2309.15813},
year = {2023}
}