Resistance between two nodes of a ring network

作者：Jiang, Zhuozhuo; Yan, Weigen^*

来源：Physica A: Statistical Mechanics and Its Applications , 2017, 484: 21-26.

DOI：10.1016/j.physa.2017.04.158

• Resistance
• Network
• Principle of elimination
• Principle of substitution

The resistance between two nodes in some resistor networks has been studied extensively by mathematicians and physicists. Given m positive integers m(1), m(2), ... , m(n) let G[m(i)](1)(n) be the resistor network with node set V = V-1 boolean OR V-2 boolean OR ... U V-n and with a unit resistor between arbitrary two nodes u is an element of V-i, nu is an element of Vi+1 for i = 1, 2, ... , where V-i boolean AND V-j = Empty set if i not equal j, and vertical bar V-i vertical bar= m(i) Vn+1 = V-1. Gervacio (2016) introduces a modified method to compute the resistance between two nodes. Based on this method, in this paper, we use the elimination and substitution principles in electrical circuit to obtain the resistance between arbitrary two nodes of G[m(i)](1)(n).

• 出版日期2017-10-15
• 单位集美大学