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- Title
SPECTRAL ANALYSIS FOR WEIGHTED LEVEL-4 SIERPIŃSKI GRAPHS AND ITS APPLICATIONS.
- Authors
ZHU, XINGCHAO; ZHU, ZHIYONG
- 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.
- Subjects
SPANNING trees; LAPLACIAN matrices; RANDOM walks; SYMBOLIC computation
- Publication
Fractals, 2023, Vol 31, Issue 5, p1
- ISSN
0218-348X
- Publication type
Article
- DOI
10.1142/S0218348X23500494