In recent years, spectrum analysis and computation have developed rapidly in order to explore and characterize the properties of network sciences. Let Ln be obtained from the transformation of the graph L6,4,4 n , which obtained by attaching crossed two four-membered rings to the terminal of crossed phenylenes. Firstly, we study the (nomalized) Laplacian spectrum of Ln based on the decomposition theorem for the corresponding matrices. Secondly, we obtain the closed-term fomulas for the (multiplicative degree) Kirchhoff index and the number of spanning trees from the relationship between roots and coefficients in linear chain networks. Finally, we are surprised to find that the (multiplicative degree) Kirchhoff index of Ln is nearly to one quarter of its (Gutman) Wiener index when n tends to infinity.

Phenylenes network is applied in several fields of chemistry sciences due to its advantages compared to other several columnar networks, recently. This paper aims to introduce a kind of networks which obtained by a family of dicyclobutadieno derivative of linear phenylene chain Ln which is made up of n hexagons and (n+1) quadrangles. Let L2n be the strong prism of the dicyclobutadieno derivative of linear phenylenes Ln. By taking full advantage of the knowleges about the normalized Laplacian spectra, we induce the explicit expressions, with respect to the index n, of the multiplicative degree-Kirchhoff index and the number of spanning tree based on the graph L2n.