Calculating two-point resistances in distance-regular resistor networks
Calculating two-point resistances in distance-regular resistor networks
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DOI：
10.1088/1751-8113/40/19/002
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发表时间：
2006-11
期刊：
影响因子：
--
通讯作者：
S. Jafarizadeh;R. Sufiani;M. Jafarizadeh
中科院分区：
文献类型：
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作者：
S. Jafarizadeh;R. Sufiani;M. Jafarizadeh
给出了一种计算任意距离规则电阻器网络中任意两个节点之间电阻的算法，其计算基于Jafarizadeh和Salimi （2006 J. Phys）中引入的分层。答:数学。gen 39 1-29)和与网络相关的频谱分布（Stieltjes函数）的Stieltjes变换。结果表明，一个节点α与属于同一层的所有节点β之间的电阻相对于α，属于第i层的β相对于α)是相同的。同时，根据网络的大小和相应的交点数，给出了两点电阻的解析表达式。特别地，用参数（v, κ, λ, μ）给出了强正则网络中的两点电阻。此外，还讨论了强正则网络中两点电阻的下界和上界。
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 Jafarizadeh and Salimi (2006 J. Phys. A: Math. Gen. 39 1–29) and the 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 , β belonging to the ith stratum with respect to the α) are the same. Also, the analytical formulae for two-point resistances , are given in terms of 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 its parameters (v, κ, λ, μ). Moreover, the lower and upper bounds for two-point resistances in strongly regular networks are discussed.