Computing the Laplacian Spectrum of Linear Octagonal-Quadrilateral Networks and Its Applications

Abstract

As a powerful tool for describing and studying the properties of compounds, the graphs spectrum analysis and calculations have attracted substantial attention of the scientific community. Let O_n denote linear octagonal-quadrilateral networks. In this paper, we investigate that the Laplacian spectrum of O_n consists of the Laplacian spectrum of $P_{4n+1}$ and eigenvalues of a symmetric tridiagonal matrix of order $4n+1.$ As applications of the obtained results, we derive the explicit closed formulas of Kirchhoff index and complexity of O_n on the basis of the relationship between the coefficients and roots of the characteristic polynomial.

Keywords:

• Laplacian matrix
• Kirchhoff index
• complexity

AMS SUBJECT CLASSIFICATION:

• 05C50
• 05C90

Acknowledgments

The authors would like to express their sincere gratitude to the editor and anonymous referees for valuable suggestions, which led to great deal of improvement of the original paper.

Additional information

Funding

This work was supported in part by National Natural Science Foundation of China Grant 11601006, and by China Postdoctoral Science Foundation under Grant 2017M621579, and by the Postdoctoral Science Foundation of Jiangsu Province under Grant 1701081B, and by the Project of Anhui Jianzhu University under Grant 2016QD116 and Grant 2017dc03 and overseas visiting and training program for outstanding young talents in Universities under Grant gxgwfx2018045.