The normalized Laplacians, degree-Kirchhoff index and the spanning trees of linear hexagonal chains
The normalized Laplacians, degree-Kirchhoff index and the spanning trees of linear hexagonal chains
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DOI：
10.1016/j.dam.2016.02.019
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发表时间：
2016-07
期刊：
影响因子：
--
通讯作者：
Jing Huang;Shuchao Li;Liqun Sun
中科院分区：
文献类型：
--
作者：
Jing Huang;Shuchao Li;Liqun Sun
设Ln是具有n个六边形的线性六边形链.本文根据图的正规化Laplacian多项式的分解定理，得到了Ln的正规化Laplacian谱由两个2n + 1阶对称三对角矩阵的特征值组成。结合这两个矩阵的特征多项式的根与系数之间的关系，给出了度-Kirchhoff指数（分别为的生成树的数目）。最后，有趣的是发现Ln的度Kirchhoff指数约为其Gutman指数的一半.
Let L n be a linear hexagonal chain with n hexagons. In this paper, according to the decomposition theorem of normalized Laplacian polynomial of a graph, we obtain that the normalized Laplacian spectrum of L n consists of the eigenvalues of two symmetric tridiagonal matrices of order 2 n+ 1. Together with the relationship between the roots and coefficients of the characteristic polynomials of the above two matrices, explicit closed formula of the degree-Kirchhoff index (resp. the number of spanning trees) of L n is derived. Finally, it is interesting to find that the degree-Kirchhoff index of L n is approximately one half of its Gutman index.