Essential Spectrum of Discrete Laplacian – Revisited

Numerical Calculation of the Essential Spectrum of a Laplacian

The Essential Spectrum of the Laplacian on Manifolds with Ends

Let V be a noncompact complete Riemannian manifold. We find a geometric condition which assures that the essential spectrum of the Laplacian on V contains a half-line, by means of fiber bundle structures and the asymptotic behavior of mean curvatures on the ends of V , and give lower bounds of the essential spectrum. Our criteria can be applied to locally symmetric spaces of finite volume and m...

Normalized laplacian spectrum of two new types of join graphs

‎Let $G$ be a graph without an isolated vertex‎, ‎the normalized Laplacian matrix $tilde{mathcal{L}}(G)$‎ ‎is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$‎, where ‎$mathcal{D}$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎G‎$‎‎. ‎The eigenvalues of‎ $tilde{mathcal{L}}(G)$ are ‎called as ‎the ‎normalized Laplacian eigenva...

Laplacian Spectrum Learning

The eigenspectrum of a graph Laplacian encodes smoothness information over the graph. A natural approach to learning involves transforming the spectrum of a graph Laplacian to obtain a kernel. While manual exploration of the spectrum is conceivable, non-parametric learning methods that adjust the Laplacian’s spectrum promise better performance. For instance, adjusting the graph Laplacian using ...

The Laplacian Spectrum of Graphs †

The paper is essentially a survey of known results about the spectrum of the Laplacian matrix of graphs with special emphasis on the second smallest Laplacian eigenvalue λ2 and its relation to numerous graph invariants, including connectivity, expanding properties, isoperimetric number, maximum cut, independence number, genus, diameter, mean distance, and bandwidth-type parameters of a graph. S...