Effective resistances and Kirchhoff index of ladder graphs


ÇINKIR Z.

JOURNAL OF MATHEMATICAL CHEMISTRY, vol.54, no.4, pp.955-966, 2016 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.1007/s10910-016-0597-8
  • Title of Journal : JOURNAL OF MATHEMATICAL CHEMISTRY
  • Page Numbers: pp.955-966

Abstract

We explicitly compute the effective resistances between any two vertices of a ladder graph by using circuit reductions. Using our findings, we obtain explicit formulas for Kirchhoff index of a ladder graph. Comparing our formula for Kirchhoff index and previous results in the literature, we obtain an explicit sum formula involving trigonometric functions. We also expressed our formulas in terms of certain generalized Fibonacci numbers that are the values of the Chebyshev polynomials of the second kind at 2.