# Computing the Laplacian spectrum of linear octagonal-quadrilateral networks and its applications

## TL;DR

This paper investigates the Laplacian spectrum of linear octagonal-quadrilateral networks using Laplacian polynomials, enabling the calculation of the Kirchhoff index and network complexity.

## Contribution

It introduces a method to determine the Laplacian spectrum and related properties for a specific class of networks, expanding spectral graph theory applications.

## Key findings

- Laplacian spectrum of Ln is characterized
- Kirchhoff index of Ln is computed
- Network complexity is derived from spectral data

## Abstract

Let Ln denote linear octagonal-quadrilateral networks. In this paper, we aim to firstly investigate the Laplacian spectrum on the basis of Laplacian polynomial of Ln. Then, by applying the relationship between the coefficients and roots of the polynomials, the Kirchhoff index and the complexity are determined.