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Spectral analysis for weighted level-3 Sierpiński graphs

Author

Listed:
  • Xingchao Zhu

    (School of Science, Northwest A&F University, Yangling, Shannxi 712100, P. R. China)

  • Zhiyong Zhu

    (School of Science, Northwest A&F University, Yangling, Shannxi 712100, P. R. China)

Abstract

The spectrum of normalized Laplacian matrix of a network has attracted more and more attention because it is related to the structural properties and dynamical aspects of the network, specially in random walks. In this paper, we study the spectra and their applications of normalized Laplacian matrices for weighted level-3 Sierpiński graphs that are constructed in an iterative way. We analytically obtain all the spectra from two successive generations by applying the decimation method. Using the obtained spectra, we then derive closed-form expressions for their eigentime identity and number of spanning trees.

Suggested Citation

  • Xingchao Zhu & Zhiyong Zhu, 2023. "Spectral analysis for weighted level-3 SierpiÅ„ski graphs," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-23, June.
  • Handle: RePEc:wsi:ijmpcx:v:34:y:2023:i:06:n:s0129183123500730
    DOI: 10.1142/S0129183123500730
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