70
Views
4
CrossRef citations to date
0
Altmetric
Research Articles

On the Laplacian Spectrum and Kirchhoff Index of Generalized Phenylenes

, ORCID Icon &
Pages 1892-1901 | Received 04 Oct 2019, Accepted 08 Dec 2019, Published online: 23 Dec 2019

References

  • H. Wiener, “Structural Determination of Paraffin Boiling Points,” Journal of the American Chemical Society 69, no. 1 (1947): 17–20.
  • D. J. Klein, and M. Randi ́c, “Resistance Distance,” Journal of Mathematical Chemistry 12, no. 1 (1993): 81–95.
  • I. Gutman and B. Mohar, “The quasi-Wiener and the Kirchhoff Indices Coincide,” Journal of Chemical Information and Computer Sciences 36, no. 5 (1996): 982–5.
  • H. Y. Zhu, D. J. Klein, and I. Lukovits, “Extensions of the Wiener Number,” Journal of Chemical Information and Computer Sciences 36, no. 3 (1996): 420–8.
  • D. J. Klein and O. Ivanciuc, “Graph Cyclicity, Excess Conductance, and Resistance Deficit,” Journal of Mathematical Chemistry 30, no. 3 (2001): 271–87.
  • S. C. Li, W. Wei, and S. Yu, “On Normalized Laplacians, Multiplicative Degree-Kirchhoff Indices, and Spanning Trees of the Linear [n]Phenylenes and Their Dicyclobutadieno Derivatives,” International Journal of Quantum Chemistry 119, no. 8 (2019): e25863.
  • J. B. Liu, J. Zhao, and Z. X. Zhu, “On the Number of Spanning Trees and Normalized Laplacain of Linear Octagonal-Quadrilateral Networks,” International Journal of Quantum Chemistry 119, no. 17 (2019): e25971.
  • J. B. Liu, C. Wang, S. Wang, and B. Wei, “Zagreb Indices and Multiplicative Zagreb Indices of Eulerian Graphs,” Bulletin of the Malaysian Mathematical Sciences Society 42, no. 1 (2019): 67–78.
  • X. Ma and H. Bian, “The Normalized Laplacians, Degree-Kirchhoff Index and the Spanning Trees of Hexagonal Mo¨ bius Graph,” Applied Mathematics and Computation 355 (2019): 33–46.
  • Y. G. Pan, J. P. Li, S. C. Li, and W. J. Luo, “On the Normalized Laplacians with Some Classical Parameters Involving Graph Transformations,” Linear and Multilinear Algebra. doi:https://doi.org/10.1080/03081087.2018.1548556
  • Y. G. Pan and J. P. Li, “Graphs That Minimizing Symmetric Division Deg Index,” MATCH Communications in Mathematical and in Computer Chemistry 82 (2019): 43–55.
  • D. J. Klein, I. Lukovits, and I. Gutman, “On the Definition of the Hyper-Wiener Index for Cycle-Containing Structures,” Journal of Chemical Information and Modeling 35 (1995): 50–2.
  • H. P. Zhang and Y. J. Yang, “Resistance Distance and Kirchhoff Index in Circulant Graphs,”International Journal of Quantum Chemistry 107, no. 2 (2007): 330–9.
  • J. Huang, S. C. Li, and X. C. Li, “The Normalized Laplacian, Degree-Kirchhoff Index and Spanning Trees of the Linear Polyomino Chains,” Applied Mathematics and Computation 289 (2016): 324–34.
  • J. Huang, S. C. Li, and L. Q. Sun, “The Normalized Laplacians, Degree-Kirchhoff Index and the Spanning Trees of Linear Hexagonal Chains,” Discrete Applied Mathematics 207 (2016): 67–79.
  • Y. J. Yang and H. P. Zhang, “Kirchhoff Index of Linear Hexagonal Chains,” International Journal of Quantum Chemistry 108, no. 3 (2008): 503–12.
  • Y. G. Pan, and J. P. Li, “Kirchhoff Index, Multiplicative degree-Kirchhoff Index and Spanning Trees of the Linear Crossed Hexagonal Chains,” International Journal of Quantum Chemistry 118, no. 24 (2018): e25787.
  • J. Zhao, J. B. Liu, and S. Hayat, “Resistance Distance-Based Invariants and the Number of Spanning Trees of Linear Crossed Octagonal Graphs,” Journal of Applied Mathematics and Computing. http:doi.org/10.1007/s12190-019-01306-6.
  • Y. J. Peng and S. C. Li, “On the Kirchhoff Index and the Number of Spanning Trees of Linear Phenylenes,” MATCH Communications in Mathematical and in Computer Chemistry 77 (2017): 765–80.
  • Z. Cinkir, “Effective Resistances and Kirchhoff Index of Ladder Graphs,” Journal of Mathematical Chemistry 54, no. 4 (2016): 955–66.
  • A. Carmona, A. M. Encinas, and M. Mitjana, “Effective Resistances for Ladderlike Chains,”International Journal of Quantum Chemistry 114, no. 24 (2014): 1670–7.
  • X. Ma and H. Bian, “The Normalized Laplacians, Degree-Kirchhoff Index and the Spanning Trees of Cylinder Phenylene Chain,” Polycyclic Aromatic Compounds. doi:https://doi.org/10.1080/10406638.2019.1665553
  • Z. X. Zhu and J. B. Liu, “The Normalized Laplacian, Degree-Kirchhoff Index and the Spanning Tree Numbers of Generalized Plenylenes,” Discrete Applied Mathematics 254 (2019): 256–67.
  • F. R. K. Chung, Spectral graph theory (Providence, RI: American Mathematical Society, 1997).
  • W. N. Anderson and T. D. Morley, “Eigenvalues of the Laplacian of a Graph,” Linear and Multilinear Algebra 18, no. 2 (1985): 141–5.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.