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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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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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
Keywords
- Resistance
- Network
- Principle of elimination
- Principle of substitution
- \(K_{m , n}\)-double star transform