The Normalized Laplacians, Degree-Kirchhoff Index and the Spanning Trees of Cylinder Phenylene Chain
The Normalized Laplacians, Degree-Kirchhoff Index and the Spanning Trees of Cylinder Phenylene Chain
复制标题
归一化拉普拉斯算子、基尔霍夫指数和圆柱亚苯基链的生成树
DOI：
10.1080/10406638.2019.1665553
复制
发表时间：
2019-09-26
影响因子：
2.4
通讯作者：
Bian, Hong
中科院分区：
文献类型：
--
作者：
Ma, Xiaoling;Bian, Hong
Let PHn denote a linear phenylene chain with n hexagons and n - 1 quadrangles. Then the cylinder phenylene chain CPn is the graph obtained from the PHn by identifying the opposite lateral edges in ordered way. In this paper, using the normalized Laplacian decomposition theorem, the normalized Laplacian spectrum of CPn consisting of the eigenvalues of two symmetric quasi-tridiagonal matrices and of order 3n is determined. Together with the relationship between the roots and coefficients of the characteristic polynomials of the above two matrices, an explicit closed-form formulas of the degree-Kirchhoff index, the Kemeny's constant and the number of spanning trees of CPn are obtained in terms of the index n.
