Computation of resistance distance and Kirchhoff index of the two classes of silicate networks

Muhammad Shoaib Sardar, Xiang-Feng Pan and Si-Ao Xu

Applied Mathematics and Computation, 2020, vol. 381, issue C

Abstract: The resistance distance between two vertices of a simple connected graph G is equal to the resistance between two equivalent points on an electrical network, constructed so as to correspond to G, with each edge being replaced by a unit resistor. The Kirchhoff index of G is the sum of resistance distances between all pairs of vertices in G. In this paper, the resistance distance between any two arbitrary vertices of a chain silicate network and a cyclic silicate network was procured by utilizing techniques from the theory of electrical networks, i.e., the series and parallel principles, the principle of elimination, the star-triangle transformation and the delta-wye transformation. Two closed formulae for the Kirchhoff index of the chain silicate network and the cyclic silicate network were obtained respectively.

Keywords: Resistance distance; Kirchhoff index; Star-triangle transformation; Delta-wye transformation; Silicate network (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:381:y:2020:i:c:s0096300320302526

DOI: 10.1016/j.amc.2020.125283

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