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On the spectrum of the normalized Laplacian of iterated triangulations of graphs

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  • Xie, Pinchen
  • Zhang, Zhongzhi
  • Comellas, Francesc

Abstract

The eigenvalues of the normalized Laplacian of a graph provide information on its topological and structural characteristics and also on some relevant dynamical aspects, specifically in relation to random walks. In this paper we determine the spectra of the normalized Laplacian of iterated triangulations of a generic simple connected graph. As an application, we also find closed-forms for their multiplicative degree-Kirchhoff index, Kemeny’s constant and number of spanning trees.

Suggested Citation

  • Xie, Pinchen & Zhang, Zhongzhi & Comellas, Francesc, 2016. "On the spectrum of the normalized Laplacian of iterated triangulations of graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1123-1129.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:1123-1129
    DOI: 10.1016/j.amc.2015.09.057
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    References listed on IDEAS

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    1. Zhang, Zhongzhi & Rong, Lili & Zhou, Shuigeng, 2007. "A general geometric growth model for pseudofractal scale-free web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 329-339.
    2. Mehatari, Ranjit & Banerjee, Anirban, 2015. "Effect on normalized graph Laplacian spectrum by motif attachment and duplication," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 382-387.
    3. Zhongzhi Zhang & Shuigeng Zhou & Lichao Chen, 2007. "Evolving pseudofractal networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(3), pages 337-344, August.
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    Citations

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    Cited by:

    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. Wang, Chengyong & Guo, Ziliang & Li, Shuchao, 2018. "Expected hitting times for random walks on the k-triangle graph and their applications," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 698-710.
    3. Sun, Shaowei & Das, Kinkar Ch., 2019. "On the second largest normalized Laplacian eigenvalue of graphs," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 531-541.
    4. 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.
    5. Cui, Shu-Yu & Tian, Gui-Xian, 2017. "The spectra and the signless Laplacian spectra of graphs with pockets," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 363-371.
    6. Xie, Pinchen & Yang, Bingjia & Zhang, Zhongzhi & Andrade, Roberto F.S., 2018. "Exact evaluation of the causal spectrum and localization properties of electronic states on a scale-free network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 40-48.
    7. 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.
    8. Liao, Yunhua & Aziz-Alaoui, M.A. & Zhao, Junchan & Hou, Yaoping, 2019. "The behavior of Tutte polynomials of graphs under five graph operations and its applications," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    9. Palacios, José Luis & Markowsky, Greg, 2021. "Kemeny’s constant and the Kirchhoff index for the cluster of highly symmetric graphs," Applied Mathematics and Computation, Elsevier, vol. 406(C).

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