Asymptotic behavior of the Kirchhoff index for square lattice with boundary conditions

Authors

FATİH ECEVİTFollow
ARZU BOYSALFollow

Author ORCID Identifier

FATİH ECEVİT: 0000-0002-6018-9699

ARZU BOYSAL: 0000-0002-9350-7163

Abstract

We determine leading asymptotic behavior of the Kirchhoff index for the square lattice under free, cylindrical and toroidal boundary conditions. Our results provide correct forms of the eleven false theorems/results published in the following papers: L. Ye, On the Kirchhoff index of some toroidal lattices, Linear Multilinear Algebra, 59:6 (2011), 645--650; J.-B. Liu, X.-F. Pan, J. Cao, X. Huang, The Kirchhoff index of toroidal meshes and variant networks, Math. Probl. Eng., Article ID 286876, 8 pages (2014); J.-B. Liu, X.-F. Pan, A unified approach to the asymptotic topological indices of various lattices, Appl. Math. Comput., 270 (2015), 62--73.

DOI

10.55730/1300-0098.3571

Keywords

Kirchhoff index, lattice sum, asymptotic approximation

First Page

18

Last Page

28

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

ECEVİT, FATİH and BOYSAL, ARZU (2025) "Asymptotic behavior of the Kirchhoff index for square lattice with boundary conditions," Turkish Journal of Mathematics: Vol. 49: No. 1, Article 3. https://doi.org/10.55730/1300-0098.3571
Available at: https://journals.tubitak.gov.tr/math/vol49/iss1/3