Effective resistances and Kirchhoff index of ladder graphs

ÇINKIR Z.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.54, sa.4, ss.955-966, 2016 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 4
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s10910-016-0597-8
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.955-966
  • Abdullah Gül Üniversitesi Adresli: Evet

Özet

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.