Spectral analysis for weighted iterated quadrilateral graphs

Meifeng Dai, Yufei Chen (), Xiaoqian Wang () and Weiyi Su ()
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Meifeng Dai: Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China
Yufei Chen: #x2020;School of Mathematical Sciences, East China Normal University, Shanghai 201100, P. R. China
Xiaoqian Wang: Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China
Weiyi Su: #x2021;Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 11, 1-20

Abstract: Much information about the structural properties and dynamical aspects of a network is measured by the eigenvalues of its normalized Laplacian matrix. In this paper, we aim to present a first study on the spectra of the normalized Laplacian matrix of weighted iterated quadrilateral graphs. We analytically obtain all the eigenvalues, as well as their multiplicities from two successive generations. As an example of application of these results, we then derive closed-form expressions for the multiplicative degree Kirchhoff index and the Kemeny’s constant, as well as the number of weighted spanning trees.

Keywords: Weighted graph; normalized Laplacian spectrum; multiplicative degree Kirchhoff index; Kemeny’s constant; number of weighted spanning trees (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0129183118501139

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