The normalized Laplacian spectrum of subdivisions of a graph

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.

References in corpus (2)

• Random walks on weighted networks
• Further applications of the Container Method

Cited by in corpus (8)

• Spectra, hitting times, and resistance distances of $q$-subdivision graphs
• Effects of heterogeneity in site-site couplings for tight-binding models on scale-invariant structures
• Upper Eigenvalue Bounds for the Kirchhoff Laplacian on Embbeded Metric Graphs
• The normalized Laplacian and related indexes of graphs with edges blew up by cliques
• Spectra of $(H_1,H_2)$-merged subdivision graph of a graph
• The normalized Laplacian spectra of subdivision vertex-edge neighbourhood vertex(edge)-corona for graphs
• The normalized Laplacians and random walks of the parallel subdivision graphs
• Edge Domination Number and the Number of Minimum Edge Dominating Sets in Pseudofractal Scale-Free Web and Sierpiński Gasket