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 On2 be the strong prism of an octagonal network On. In this study, using the normalized Laplacian decomposition theorem, we determine the normalized Laplacian spectrum of On2 which consists of the eigenvalues of matrices ℒA and ℒS of order 3n+1. As applications of the obtained results, the explicit formulae of the degree-Kirchhoff index and the number of spanning trees for On2 are on the basis of the relationship between the roots and coefficients.