Calculating two-point resistances in distance-regular resistor networks

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dc.creatorJafarizadeh, M. A.
dc.creatorSufiani, R.
dc.creatorJafarizadeh, S.
dc.date2006-11-27
dc.date.accessioned2026-07-07T07:31:29Z
dc.date.available2026-07-07T07:31:29Z
dc.descriptionAn 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
dc.description30 pages
dc.identifierhttps://arxiv.org/abs/cond-mat/0611683
dc.identifierhttp://arxiv.org/abs/cond-mat/0611683
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/118772
dc.subjectStatistical Mechanics
dc.titleCalculating two-point resistances in distance-regular resistor networks
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