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Spectral Analysis For Weighted Level-4 Sierpiåƒski Graphs And Its Applications

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

Much information on the structural properties and some relevant dynamical aspects of a graph can be provided by its normalized Laplacian spectrum, especially for those related to random walks. In this paper, we aim to present a study on the normalized Laplacian spectra and their applications of weighted level-4 Sierpiński graphs. By using the spectral decimation technique and a theoretical matrix analysis that is supported by symbolic and numerical computations, we obtain a relationship between the normalized Laplacian spectra for two successive generations. Applying the obtained recursive relation, we then derive closed-form expressions of Kemeny’s constant and the number of spanning trees for the weighted level-4 Sierpiński graph.

Suggested Citation

  • Xingchao Zhu & Zhiyong Zhu, 2023. "Spectral Analysis For Weighted Level-4 Sierpiåƒski Graphs And Its Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-20.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:05:n:s0218348x23500494
    DOI: 10.1142/S0218348X23500494
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