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

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 On denote linear octagonal-quadrilateral networks. In this paper, we investigate that the Laplacian spectrum of On consists of the Laplacian spectrum of P4n+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 On on the basis of the relationship between the coefficients and roots of the characteristic polynomial.