SPECTRAL ANALYSIS FOR WEIGHTED LEVEL-4 SIERPIŃSKI GRAPHS AND ITS APPLICATIONS

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

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-20

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.

Keywords: Fractal; Weighted Graph; Weighted Level-4 Sierpiński Graph; Normalized Laplacian Spectrum; Kemeny’s Constant; Spanning Trees (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500494

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