Cinkir, Zubeyir2021-10-012021-10-0120160259-97911572-8897https://doi.org/10.1007/s10910-016-0597-8https://hdl.handle.net/20.500.12573/975This work is supported by The Scientific and Technological Research Council of Turkey-TUBITAK ( Project No: 110T686) and by BAGEP of The Science Academy.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.enginfo:eu-repo/semantics/closedAccessCircuit reductionKirchhoff indexEffective resistanceLadder grapharticleVolume 54 Issue 4 Page 955-966