Topological indices of linear crossed phenylenes with respect to their Laplacian and normalized Laplacian spectrum

Abstract

As a powerful tool for describing and studying the properties of networks, the graph spectrum analyses and calculations have attracted substantial attention from the scientific community. Let $ C_{n} $ represent linear crossed phenylenes. Based on the Laplacian (normalized Laplacian, resp.) polynomial of $ C_{n} $, we first investigated the Laplacian (normalized Laplacian, resp) spectrum of $ C_{n} $ in this paper. Furthermore, the Kirchhoff index, multiplicative degree-Kirchhoff, index and complexity of $ C_{n} $ were obtained through the relationship between the roots and the coefficients of the characteristic polynomials. Finally, it was found that the Kirchhoff index and multiplicative degree-Kirchhoff index of $ C_{n} $ were approximately one quarter of their Wiener index and Gutman index, respectively.

Keywords

• laplacian spectrum
• normalized laplacian spectrum
• kirchhoff index
• multiplicative degree-kirchhoff index
• complexity