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The normalized Laplacians, degree-Kirchhoff index and the spanning trees of hexagonal Möbius graphs

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  • Ma, Xiaoling
  • Bian, Hong

Abstract

Let HMn be a hexagonal Möbius 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 LA and LS 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.

Suggested Citation

  • Ma, Xiaoling & Bian, Hong, 2019. "The normalized Laplacians, degree-Kirchhoff index and the spanning trees of hexagonal Möbius graphs," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 33-46.
    • Handle: RePEc:eee:apmaco:v:355:y:2019:i:c:p:33-46
    DOI: 10.1016/j.amc.2019.02.052
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    References listed on IDEAS

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    1. Huang, Jing & Li, Shuchao & Li, Xuechao, 2016. "The normalized Laplacian, degree-Kirchhoff index and spanning trees of the linear polyomino chains," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 324-334.
    2. Li, Deqiong & Hou, Yaoping, 2017. "The normalized Laplacian spectrum of quadrilateral graphs and its applications," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 180-188.
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    Cited by:

    1. Sardar, Muhammad Shoaib & Pan, Xiang-Feng & Xu, Si-Ao, 2020. "Computation of resistance distance and Kirchhoff index of the two classes of silicate networks," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    2. Jia-Bao Liu & Jing Zhao & Zhongxun Zhu & Jinde Cao, 2019. "On the Normalized Laplacian and the Number of Spanning Trees of Linear Heptagonal Networks," Mathematics, MDPI, vol. 7(4), pages 1-15, March.

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