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

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.