The normalized Laplacian spectrum of subdivisions of a graph

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2016Embargo end date: 01 Jan 2015 English Publisher:Elsevier BVJournal:Applied Mathematics and Computation, volume 286, pages 250-256 (issn: 0096-3003,

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Authors: Xie, Pinchen; Zhang, Zhongzhi; Comellas Padró, Francesc de Paula;

doi: 10.1016/j.amc.2016.04.033 , 10.48550/arxiv.1510.02394

arXiv: 1510.02394

handle: 2117/104267

The normalized Laplacian spectrum of subdivisions of a graph

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Abstract

Determining and analyzing the spectra of graphs is an important and exciting research topic in theoretical computer science. The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on some relevant dynamical aspects, in particular those related to random walks. In this paper, we give the spectra of the normalized Laplacian of iterated subdivisions of simple connected graphs. As an example of application of these results we find the exact values of their multiplicative degree-Kirchhoff index, Kemeny's constant and number of spanning trees.

Related Organizations

Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain
Fudan University
China (People's Republic of)
Universitat Polit?cnica de Catalunya
Spain

Keywords

Subdivision graph, Spanning trees, degree-Kirchhoff index, normalized Laplacian spectrum, FOS: Physical sciences, Kemeny's constant, Graph theory--Data processing, Transformacions de, FOS: Mathematics, Mathematics - Combinatorics, Degree-Kirchhoff index, Condensed Matter - Statistical Mechanics, Mathematical Physics, subdivision graph, Àrees temàtiques de la UPC::Matemàtiques i estadística, Normalized Laplacian spectrum, Statistical Mechanics (cond-mat.stat-mech), Graphs and linear algebra (matrices, eigenvalues, etc.), Laplace, :Matemàtiques i estadística [Àrees temàtiques de la UPC], Mathematical Physics (math-ph), spanning trees, Kemeny’s constant, Laplace, Transformacions de, Combinatorics (math.CO)

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