On Normalized Laplacian, Degree-Kirchhoff Index of the Strong Prism of Generalized Phenylenes*

The eigenvalues of normalized Laplacian are extremely important for analyzing the structure properties of non-regular graphs. A molecular graph of generalized phenylene Ln is a linear chain containing n hexagons and n quadrangles. The strong prism of a graph G is the strong product of the complete graph of order 2 and G. Let Ln2 be the strong prism of generalized phenylene Ln. In this paper, the normalized Laplacian spectra of Ln2 were scrutinized by using decomposition theorem for the corresponding matrices. Further, the explicit formulae of the degree-Kirchhoff index and the number of spanning trees for Ln2 were obtained.