Resistance determination of the decorated triangular and honeycomb lattices

By employing the lattice Green’s function method, we study the resistance between any two lattice sites of infinite, decorated triangular and honeycomb (hexagonal) lattices of identical resistors. In addition, we expressed the resistance for these lattices in terms of the one for the triangular lattice. Finally, we obtained the asymptotic behaviors of the resistance for large separations between lattice sites.