Asymptotic behavior of the Kirchhof index for square lattice with boundary conditions
Turkish Journal of Mathematics, cilt.49, sa.1, ss.18-28, 2025 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 49 Sayı: 1
- Basım Tarihi: 2025
- Doi Numarası: 10.55730/1300-0098.3571
- Dergi Adı: Turkish Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.18-28
- Anahtar Kelimeler: Kirchhoff index, lattice sum, asymptotic approximation
- Boğaziçi Üniversitesi Adresli: Evet
Özet
We determine the leading asymptotic behavior of the Kirchhof 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, Applied Mathematics and Computation, 270 (2015), 62–73.