Computing the Normalized Laplacian Spectrum and Spanning Tree of the Strong Prism of Octagonal Network

Abstract

Spectrum analysis and computing have expanded in popularity in recent years as a critical tool for studying and describing the structural properties of molecular graphs. Let O n 2 be the strong prism of an octagonal network O n . In this study, using the normalized Laplacian decomposition theorem, we determine the normalized Laplacian spectrum of O n 2 which consists of the eigenvalues of matrices ℒ A and ℒ S of order 3 n + 1 . As applications of the obtained results, the explicit formulae of the degree-Kirchhoff index and the number of spanning trees for O n 2 are on the basis of the relationship between the roots and coefficients.