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.

Computing the Laplacian spectrum and Wiener index of pentagonal-derivation cylinder/Möbius network

“…It provides a unique way of measuring the relationship between nodes and has applications in different fields, including mathematics, physics, social networks, chemistry, and transportation systems. In the past two decades, numerous researchers have established explicit formulae of Kirchhoff indices for various kind of graphs, such as möbius hexagonal chain [7] , [8] , cylinder/möbius octagonal chain [9] , [10] , linear pentagonal chain [11] , penta-graphene [12] , pentagonal-quadrilateral network [13] , generalized phenylene [14] , [15] , crossed octagonal [16] , linear heptagonal network [17] , [18] , cylinder phenylene chain [19] , strong prism [20] , [21] and so on (see more [22] , [23] , [24] , [25] , [26] ).…”