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The normalized Laplacian spectrum of subdivisions of a graph

Author

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

Abstract

Determining and analyzing the spectra of graphs is an important and exciting research topic in mathematics science and theoretical computer science. The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on some relevant dynamical aspects, in particular those related to random walks. In this paper, we give the spectra of the normalized Laplacian of iterated subdivisions of simple connected graphs. As an example of application of these results we find the exact values of their multiplicative degree-Kirchhoff index, Kemeny’s constant and number of spanning trees.

Suggested Citation

  • Xie, Pinchen & Zhang, Zhongzhi & Comellas, Francesc, 2016. "The normalized Laplacian spectrum of subdivisions of a graph," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 250-256.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:250-256
    DOI: 10.1016/j.amc.2016.04.033
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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. 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).
    7. Zong, Yue & Dai, Meifeng & Wang, Xiaoqian & He, Jiaojiao & Zou, Jiahui & Su, Weiyi, 2018. "Network coherence and eigentime identity on a family of weighted fractal networks," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 184-194.

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