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...

Limit points for the positive eigenvalues of the normalized Laplacian matrix of a graph are considered. Specifically, it is shown that the set of limit points for the j-th smallest such eigenvalues is equal to [0, 1], while the set of limit points for the j-th largest such eigenvalues is equal to [1, 2]. Limit points for certain functions of the eigenvalues, motivated by considerations for rand...

Recognition of human pose is an actual problem in computer vision. To increase the reliability of the recognition it is proposed to use structured information in the form of graphs. The spectrum of graphs is applied for the comparison of the structures. Image skeletonization is used to construct graphs. Line segments are the nodes of the graph. The end point of line segments are the edges of th...

The main aim of this study is to characterize new classes of multicone graphs which are determined by their signless Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let C and K w denote the Clebsch graph and a complete graph on w vertices, respectively. In this paper, we show that the multicone graphs K w ▽C are determined by their signless ...

A Laplacian matrix, L = (lij) ∈ R , has nonpositive off-diagonal entries and zero row sums. As a matrix associated with a weighted directed graph, it generalizes the Laplacian matrix of an ordinary graph. A standardized Laplacian matrix is a Laplacian matrix with − 1 n ≤ lij ≤ 0 at j 6= i. We study the spectra of Laplacian matrices and relations between Laplacian matrices and stochastic matrice...

Let G be a nonsingular connected mixed graph. We determine the mixed graphs G on at least seven vertices with exactly two Laplacian eigenvalues greater than 2. In addition, all mixed graphs G with exactly one Laplacian eigenvalue greater than 2 are also characterized. c © 2006 Elsevier Ltd. All rights reserved.