On the number of spanning trees and normalized Laplacian of linear octagonal‐quadrilateral networks

The normalized Laplacian makes a great contribution on analyzing the structure properties of nonregular graphs. Let O n be a linear octagonal‐quadrilateral network. In this article, we first concern the normalized Laplacian spectrum of O n based on the decomposition theorem for the corresponding matrices. Then we derive the closed‐term formulas of the degree‐Kirchhoff index and the number of spanning trees of linear octagonal‐quadrilateral networks on the basis of the relations between the roots and coefficients, respectively.