For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalised Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite subgraphs. Our results are applied to some graphs with degree sequences approximately following a pow...

Let G be a simple connected graph with n ≤ 2 vertices and m edges, and let μ1 ≥ μ2 ≥...≥μn-1 >μn=0 be its Laplacian eigenvalues. The Kirchhoff index and Laplacian-energy-like invariant (LEL) of graph G are defined as Kf(G)=nΣi=1n-1<...

Let G be a graph; its Laplacian matrix is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. In this paper, we present a sharp upper bound for the Laplacian spectral radius of a tree in terms of the matching number and number of vertices, and deduce from that the largest few Laplacian spectral radii over the class of trees on a given number of vertices. © 2003...

in this paper, we study the multiplicity of positive solutions for the laplacian systems with sign-changing weight functions. using the decomposition of the nehari manifold, we prove that an elliptic system has at least two positive solutions.

Conventional electroencephalography with disc electrodes has major drawbacks including poor spatial resolution, selectivity and low signal-to-noise ratio that are critically limiting its use. Concentric ring electrodes, consisting of several elements including the central disc and a number of concentric rings, are a promising alternative with potential to improve all of the aforementioned aspec...

Brain-computer interface (BCI) systems frequently use signal processing methods, such as spatial filtering, to enhance performance. The surface Laplacian can reduce spatial noise and aid in identification of sources. In BCI research, these two functions of the surface Laplacian correspond to prediction accuracy and signal orthogonality. In the present study, an off-line analysis of data from a ...

We construct two infinite families of trees that are pairwise cospectral with respect to the normalized Laplacian. We also use the normalized Laplacian applied to weighed graphs to give new constructions of cospectral pairs of bipartite unweighted graphs.

In this paper, we investigate connected nonregular graphs with four distinct Laplacian eigenvalues. We characterize all such graphs which are bipartite or have exactly one multiple Laplacian eigenvalue. Other examples of interest are also presented.

We consider the p–Laplacian operator on a domain equipped with a Finsler metric. After deriving and recalling relevant properties of its first eigenfunction for p > 1, we investigate the limit problem as p → 1.

Given a C-function f on a compact riemannian manifold (X, g) we give a set of frequencies L = Lf (ε) depending on a small parameter ε > 0 such that the relative L-error ‖f−f ‖ ‖f‖ is bounded above by ε, where f L denotes the L-partial sum of the Fourier series f with respect to an orthonormal basis of L(X) constituted by eigenfunctions of the Laplacian operator ∆ associated to the metric g.