SPECTRAL ANALYSIS FOR WEIGHTED ITERATED TRIANGULATIONS OF GRAPHS

被引：22

作者：

Chen, Yufei ^{[1
]}

Dai, Meifeng ^{[1
]}

Wang, Xiaoqian ^{[1
]}

Sun, Yu ^{[1
]}

Su, Weiyi ^{[2
]}

机构：

[1] Jiangsu Univ, Inst Appl Syst Anal, Zhenjiang 212013, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2018年 / 26卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Weighted Graph; Normalized Laplacian Spectrum; Kirchhoff Index; Kemeny's Constant; Weighted Spanning Trees; KEMENYS CONSTANT; NETWORKS; LAPLACIAN;

D O I：

10.1142/S0218348X18500172

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 of weighted iterated triangulations of 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 their multiplicative Kirchhoff index, Kemeny's constant and number of weighted spanning trees.

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