The normalized Laplacian spectrum of subdivisions of a graph

Pinchen Xie, Zhongzhi Zhang and Francesc Comellas

Applied Mathematics and Computation, 2016, vol. 286, issue C, 250-256

Abstract: Determining and analyzing the spectra of graphs is an important and exciting research topic in mathematics science and 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.

Keywords: Normalized Laplacian spectrum; Subdivision graph; Degree-Kirchhoff index; Kemeny’s constant; Spanning trees (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:286:y:2016:i:c:p:250-256

DOI: 10.1016/j.amc.2016.04.033

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