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On the Normalized Laplacian and the Number of Spanning Trees of Linear Heptagonal Networks

Author

Listed:
  • Jia-Bao Liu

    (School of Mathematical Sciences, Anhui Jianzhu University, Hefei 230601, China
    School of Mathematics, Southeast University, Nanjing 210096, China)

  • Jing Zhao

    (School of Mathematical Sciences, Anhui Jianzhu University, Hefei 230601, China)

  • Zhongxun Zhu

    (Department of Mathematics and Statistics, South Central University for Nationalities, Wuhan 430074, China)

  • Jinde Cao

    (School of Mathematics, Southeast University, Nanjing 210096, China)

Abstract

The normalized Laplacian plays an important role on studying the structure properties of non-regular networks. In fact, it focuses on the interplay between the structure properties and the eigenvalues of networks. Let H n be the linear heptagonal networks. It is interesting to deduce the degree-Kirchhoff index and the number of spanning trees of H n due to its complicated structures. In this article, we aimed to first determine the normalized Laplacian spectrum of H n by decomposition theorem and elementary operations which were not stated in previous results. We then derived the explicit formulas for degree-Kirchhoff index and the number of spanning trees with respect to H n .

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:314-:d:217931
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Huang, Jing & Li, Shuchao, 2018. "The normalized Laplacians on both k-triangle graph and k-quadrilateral graph with their applications," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 213-225.
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