The normalized Laplacians, degree-Kirchhoff index and the spanning trees of hexagonal Mobius graphs
The normalized Laplacians, degree-Kirchhoff index and the spanning trees of hexagonal Mobius graphs
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归一化拉普拉斯算子、基尔霍夫指数和六角莫比乌斯图的生成树
DOI：
10.1016/j.amc.2019.02.052
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发表时间：
2019-08-15
影响因子：
4
通讯作者：
Bian, Hong
中科院分区：
文献类型：
--
作者：
Ma, Xiaoling;Bian, Hong
令 HMn 为长度为 n 的六边形莫比乌斯图。本文根据归一化拉普拉斯多项式分解定理，得到HMn的归一化拉普拉斯谱由两个2n阶对称准三对角矩阵L-A和L-S的特征值组成。最后，利用上述两个矩阵的特征多项式的根与系数之间的关系，给出了以指数n表示的基尔霍夫指数和HMn的生成树数的显式闭公式。 (C) 2019 Elsevier Inc. 保留所有权利。
Let HMn be a hexagonal Mobius graph of length n. In this paper, due to the normalized Laplacian polynomial decomposition theorem, we obtain that the normalized Laplacian spectrum of HMn consists of the eigenvalues of two symmetric quasi-tridiagonal matrices L-A and L-S of order 2n. Finally, by applying the relationship between the roots and coefficients of the characteristic polynomials of the above two matrices, explicit closed formulas of the degree-Kirchhoff index and the number of spanning trees of HMn are given in terms of the index n. (C) 2019 Elsevier Inc. All rights reserved.