Computation of Kirchhoff Index in Generalized Ladders

Lei Zhang, Haizhen Ren
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Abstract

A connected graph G is viewed as an electrical network N by replacing each edge of G with a unit resistor. The Kirchhoff index of G is a structure-descriptor based on effective resistance of N. The generalized ladder is a subdivision graph of ladder graph. By using the properties of the Chebyshev polynomials, Laplace Theorem and so on, we obtained closed form expressions of Kirchhoff indexes for the generalized straight and generalized cyclic ladders, which generalize the results of linear quadrangular chain and linear hexagonal chain.
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广义阶梯中Kirchhoff指数的计算
通过用一个单位电阻代替G的每条边,将连通图G看作一个电网络N。G的Kirchhoff指数是基于n的有效阻力的结构描述子,广义阶梯图是阶梯图的细分图。利用切比雪夫多项式和拉普拉斯定理等性质,得到了广义直梯和广义环梯的Kirchhoff指标的封闭表达式,推广了线性四边形链和线性六边形链的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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