Abstract

In this paper, we investigate the two-vertex resistance on four Archimedean lattices. This technique is based on the Green's function corresponding to the Laplacian matrix of the lattice. The Laplacian matrix of the resistor network is determined by applying basic principles (Kirchhoff's and Ohm's laws) in electrical circuit analysis, and Fourier transforms of the electric potential and current. We present some numerical results regarding the resistance between nearby lattice vertices.

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