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

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-[Formula: see text] 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-[Formula: see text] Sierpiński graph.