This paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  We use variational methods to investigateseveral aspects of propagating waves, including localization (seeFigure 1), existence criteria and the formulas to find them. Weapproach the problem using two complementary methods: Thevariational methods fo...

In this note we address the problem of graph isomorphism by means of eigenvalue spectra of different matrix representations: the neighborhood matrix M̂ , its corresponding signless Laplacian QM̂ , and the set of higher order adjacency matrices M`s. We find that, in relation to graphs with at most 10 vertices, QM̂ leads to better results than the signless Laplacian Q; besides, when combined with M̂ ...

This paper studies the Laplacian operator on a metrized graph, and its spectral theory.

The question of deciding whether or not a given graph is Hamiltonian is a very difficult one; indeed, determining whether a given graph is Hamiltonian is NP-complete. Here, we discuss applications of spectral graph theory to this problem. In particular, we explore results by Fiedler and Nikiforov [2] regarding spectral conditions on the adjacency matrix to ensure Hamiltonicity, and results by B...

These are lecture notes that are based on the lectures from a class I taught on the topic of Spectral Graph Methods at UC Berkeley during the Spring 2015 semester. Spectral graph techniques are remarkably broad, they are widely-applicable and often very useful, and they also come with a rich underlying theory, some of which provides a very good guide to practice. Spectral graph theory is often ...

This work concerns solutions of the heat equation with spectral graph method, for which temperature is defined at discrete points in domain and spatial relationship among described by a graph. The on solved using matrix techniques involving eigenvectors eigenvalues Laplacian matrix. approach precludes computationally intensive meshing numerous time-integration steps finite element method. In pr...

We develop a nonlinear spectral graph theory, in which the Laplace operator is replaced by the 1Laplacian. The eigenvalue problem is to solve a nonlinear system involving a set valued function. In the study, we investigate the structure of the solutions, the minimax characterization of eigenvalues, the multiplicity theorem, etc. The graphic feature of eigenvalues are also studied. In particular...