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Resistance Between Two Nodes of a Ring Clique Network

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Abstract

The resistance between two nodes in some resistor networks has been studied extensively by mathematicians and physicists. Given n positive integers \(a_1,a_2,\ldots ,a_n\), let \(H[a_i]_{1}^n\) be the resistor network obtained from the complete graphs \(K_{a_i}\) by adding edges connecting every vertex in \(K_{a_i}\) to every vertex in \(K_{a_{i-1}}\) and \(K_{a_{i+1}}\), where \(i=1,2,\ldots , n\), \(K_{a_{n+1}}=K_{a_1}\), with a unit resistor between arbitrary two adjacent nodes in \(H[a_i]_{1}^n\). In this paper, using the elimination and substitution principles and some equivalent transformations in electrical circuit, we obtain explicit formula for the resistance between arbitrary two nodes of \(H[a_i]_{1}^n\).

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Data Availability Statement

No data, models or code were generated or used during the study (e.g., opinion or dataless paper).

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Acknowledgements

We are grateful to the anonymous referees for many friendly and helpful revising suggestions that greatly improved the presentation of the paper. This work was supported by the National Natural Science Foundation of China (Nos. 11701324 and 12101126), the Natural Science Foundation of Fujian Province, China (No. 2021J05185) and the Education Scientific Research Fund for Young and Middle-aged Teachers of Fujian Province (No. JAT190066).

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Authors and Affiliations

  1. School of Mathematical and Computer Sciences, Quanzhou Normal University, Quanzhou, 362000, China

    Shuli Li

  2. College of Mathematics and Informatics, Fujian Normal University, Fuzhou, 350117, China

    Tao Tian

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  1. Shuli Li
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  2. Tao Tian
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Correspondence to Tao Tian.

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Li, S., Tian, T. Resistance Between Two Nodes of a Ring Clique Network. Circuits Syst Signal Process 41, 1287–1298 (2022). https://doi.org/10.1007/s00034-021-01859-7

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  • DOI: https://doi.org/10.1007/s00034-021-01859-7

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