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Resistance between two nodes of a ring network

Author

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  • Jiang, Zhuozhuo
  • Yan, Weigen

Abstract

The resistance between two nodes in some resistor networks has been studied extensively by mathematicians and physicists. Given m positive integers m1,m2,⋯,mn, let G[mi]1n be the resistor network with node set V=V1∪V2∪⋯∪Vn and with a unit resistor between arbitrary two nodes u∈Vi,v∈Vi+1 for i=1,2,⋯,n, where Vi∩Vj=0̸ if i≠j, and ∣Vi∣=mi,Vn+1=V1. 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[mi]1n.

Suggested Citation

  • Jiang, Zhuozhuo & Yan, Weigen, 2017. "Resistance between two nodes of a ring network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 21-26.
    • Handle: RePEc:eee:phsmap:v:484:y:2017:i:c:p:21-26
    DOI: 10.1016/j.physa.2017.04.158
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    Citations

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    Cited by:

    1. Sajjad, Wasim & Sardar, Muhammad Shoaib & Pan, Xiang-Feng, 2024. "Computation of resistance distance and Kirchhoff index of chain of triangular bipyramid hexahedron," Applied Mathematics and Computation, Elsevier, vol. 461(C).
    2. Fan, Jiaqi & Zhu, Jiali & Tian, Li & Wang, Qin, 2020. "Resistance Distance in Potting Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Huang, Sumin & Li, Shuchao, 2020. "On the resistance distance and Kirchhoff index of a linear hexagonal (cylinder) chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    4. Jiang, Zhuozhuo & Yan, Weigen, 2019. "Resistances between two nodes of a path network," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 42-46.
    5. Sardar, Muhammad Shoaib & Pan, Xiang-Feng & Xu, Si-Ao, 2020. "Computation of resistance distance and Kirchhoff index of the two classes of silicate networks," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    6. Yang, Yujun & Cao, Yuliang & Yao, Haiyuan & Li, Jing, 2018. "Solution to a conjecture on a Nordhaus–Gaddum type result for the Kirchhoff index," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 241-249.
    7. Sardar, Muhammad Shoaib & Pan, Xiang-Feng & Xu, Shou-Jun, 2024. "Computation of the resistance distance and the Kirchhoff index for the two types of claw-free cubic graphs," Applied Mathematics and Computation, Elsevier, vol. 473(C).

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