2006/11/27 by M. A. Jafarizadeh, Jafarizadeh, M. A., R. Sufiani +4
Materials Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Graph theory and applications #Semiconductor materials and interfaces #Statistical Mechanics (cond-mat.stat-mech) #Synthesis and properties of polymers #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0611683
30 pages
arxiv created 2006/11/27 · openalex publication_date 2006/11/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citejs 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 (Rαβ(i), β belonging to the i-th stratum with respect to the α) are the same. Also, the analytical formulas for two-point resistances Rαβ(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