On the spectra of Markov matrices for weighted Sierpinski graphs

Relevant information from networked systems can be obtained by analyzing the spectra of matrices associated to their graph representations. In particular, the eigenvalues and eigenvectors of the Markov matrix and related Laplacian and normalized Laplacian matrices allow the study of structural and dynamical aspects of a network, like its synchronizability and random walks properties. In this study we obtain, in a recursive way, the spectra of Markov matrices of a family of rotationally invariant weighted Sierpinski graphs. From them we find analytic expressions for the weighted count of spanning trees and the random target access time for random walks on this family of weighted graphs.Postprint (published version

The normalized Laplacian spectrum of subdivisions of a graph

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.Postprint (published version

A better Wales A consultation paper on values, service priorities and spending plans

English/Welsh text on inverted pagesAvailable from British Library Document Supply Centre-DSC:f99/3676 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

On the spectrum of the normalized Laplacian of iterated triangulations of graphs

The eigenvalues of the normalized Laplacian of a graph provide information on its topological and structural characteristics and also on some relevant dynamical aspects, specifically in relation to random walks. In this paper we determine the spectra of the normalized Laplacian of iterated triangulations of a generic simple connected graph. As an application, we also find closed-forms for their multiplicative degree-Kirchhoff index, Kemeny's constant and number of spanning trees

The normalized Laplacian spectrum of subdivisions of a graph

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