Two-point resistances in an Apollonian network.

Shangguan, Yingmin; Chen, Haiyan · Phys Rev E · 2017

basic_science · Level V

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Abstract

The computation of resistance between two nodes in a resistor network is a classical problem in electric theory and graph theory. Based on the Apollonian packing, Andrade et al. introduced a deterministic growing type of networks A(k) [Phys. Rev. Lett. 94, 018702 (2005)PRLTAO0031-900710.1103/PhysRevLett.94.018702]. In this paper, first, a recursive algorithm for computing resistance between any two nodes in A(k) is given. Then as explanations, using the algorithm, explicit expressions for some resistances in A(k) are obtained.