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Calculating two-point resistances in distance-regular resistor networks

M. A. Jafarizadeh·R. Sufiani·S. Jafarizadeh
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Abstract

An algorithm for the calculation of the resistance between two arbitrary nodes in an arbitrary distance-regular resistor network is provided, where the calculation is based on stratification introduced in \cite{js} and Stieltjes transform of the spectral distribution (Stieltjes function) associated with the network. It is shown that the resistances between a node $α$ and all nodes $β$ belonging to the same stratum with respect to the $α$ ($R_{αβ^{(i)}}$, $β$ belonging to the $i$-th stratum with respect to the $α$) are the same. Also, the analytical formulas for two-point resistances $R_{αβ^{(i)}}, i=1,2,3$ are given in terms of the the size of the network and corresponding intersection numbers. In particular, the two-point resistances in a strongly regular network are given in terms of the its parameters ($v,κ,λ,μ$). Moreover, the lower and upper bounds for two-point resistances in strongly regular networks are discussed. Keywords:two-point resistance, association scheme, distance-regular networks, Stieltjes function PACs Index: 01.55.+b, 02.10.Yn

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M. A. Jafarizadeh, R. Sufiani, S. Jafarizadeh. 2006-11-27. Calculating two-point resistances in distance-regular resistor networks. https://arxiv.org/abs/cond-mat/0611683

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