Abstract
The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. Let \(B_n\) denote the linear polyomino chain with \(n-1\) squares. In this paper, first by using resistance sum rules along with series and parallel principles, explicit formulae for the resistance distances between any two vertices of \(B_n\) are given. Then based on these formulae, the largest and the smallest resistance distances in \(B_n\) are determined. Finally, the monotonicity and some asymptotic properties of resistance distances in \(B_n\) are given.
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The authors are indebted to the anonymous referees for their valuable comments and suggestions, which led to an improvement of the original manuscript.
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This work is supported by the National Natural Science Foundation of China (Grants 11571139, 11301217) and the Natural Science Foundation of Fujian Province, China (Grants 2015J01017, 2013J01014).
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Shi, L., Chen, H. Resistance distances in the linear polyomino chain. J. Appl. Math. Comput. 57, 147–160 (2018). https://doi.org/10.1007/s12190-017-1099-y
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DOI: https://doi.org/10.1007/s12190-017-1099-y