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Spectral analysis for weighted iterated quadrilateral graphs

Author

Listed:
  • Meifeng Dai

    (Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China)

  • Yufei Chen

    (#x2020;School of Mathematical Sciences, East China Normal University, Shanghai 201100, P. R. China)

  • Xiaoqian Wang

    (Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China)

  • Weiyi Su

    (#x2021;Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China)

Abstract

Much information about the structural properties and dynamical aspects of a network is measured by the eigenvalues of its normalized Laplacian matrix. In this paper, we aim to present a first study on the spectra of the normalized Laplacian matrix of weighted iterated quadrilateral graphs. We analytically obtain all the eigenvalues, as well as their multiplicities from two successive generations. As an example of application of these results, we then derive closed-form expressions for the multiplicative degree Kirchhoff index and the Kemeny’s constant, as well as the number of weighted spanning trees.

Suggested Citation

  • Meifeng Dai & Yufei Chen & Xiaoqian Wang & Weiyi Su, 2018. "Spectral analysis for weighted iterated quadrilateral graphs," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(11), pages 1-20, November.
    • Handle: RePEc:wsi:ijmpcx:v:29:y:2018:i:11:n:s0129183118501139
    DOI: 10.1142/S0129183118501139
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    Citations

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    Cited by:

    1. Liu, Jia-Bao & Zhao, Jing & Cai, Zheng-Qun, 2020. "On the generalized adjacency, Laplacian and signless Laplacian spectra of the weighted edge corona networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. Dai, Meifeng & Dai, Changxi & Ju, Tingting & Shen, Junjie & Sun, Yu & Su, Weiyi, 2019. "Mean first-passage times for two biased walks on the weighted rose networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 268-278.
    3. 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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