Spectral analysis for weighted level-3 Sierpiński graphs

Xingchao Zhu () and Zhiyong Zhu
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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

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 06, 1-23

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.

Keywords: Weighted graph; weighted level-3 Sierpiński graph; normalized Laplacian spectrum; eigentime identity; spanning trees (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0129183123500730

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