On the Laplacian Spectrum and Kirchhoff Index of Generalized Phenylenes

Abstract

Hexagonal and quadrilateral structures are very common in the molecular structure of organic chemistry, especially in polycyclic aromatic compounds. Let L_n be a generalized phenylene with t hexagons and t quadrangles, where $n=3t+1.$ Zhu and Liu (2018) determined the normalized Laplacian spectrum and then gave the explicit formulas of the multiplicative degree-Kirchhoff index and the number of spanning trees of L_n, respectively. In this article, we completely determine the Laplacian spectrum and Kirchhoff index of L_n. Moreover, we show that the Kirchhoff index of L_n is nearly one half of its Wiener index.

Keywords:

• Generalized phenylenes
• Kirchhoff index
• Laplacian spectrum
• spanning tree
• Wiener index

AMS SUBJECT CLASSIFICATION:

• 05C50
• 05C99

Acknowledgements

The authors would like to express their sincere gratitude to all the referees for their careful reading and insightful suggestions.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (61773020, 11871206).