The family G of connected graphs with second largest Laplacian eigenvalue at most θ, where θ = 3.2470 is the largest root of the equation μ−5μ+6μ−1 = 0, is characterized by Wu, Yu and Shu [Y.R. Wu, G.L. Yu and J.L. Shu, Graphs with small second largest Laplacian eigenvalue, European J. Combin. 36 (2014) 190–197]. Let G(a, b, c, d) be a graph with order n = 2a + b + 2c + 3d + 1 that consists of ...

Let G be a connected simple graph. The relationship between the third smallest eigenvalue of the Laplacian matrix and the graph structure is explored. For a tree the complete description of the eigenvector corresponding to this eigenvalue is given and some results about the multiplicity of this eigenvalue are given.

Spectral techniques are often used to partition the set of vertices a graph, or form clusters. They based on Laplacian matrix. These allow easily integrate weights edges. In this work, we introduce p-Laplacian, generalized matrix with potential, which also allows us take into account vertices. vertex independent edge weights. way, can cluster importance vertices, assigning more weight some than...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 2 June 2020Accepted: 16 September 2021Published online: 05 January 2022Keywordseigenvalue problem, domain decomposition, dimension reduction, subspace methodAMS Subject Headings65F15Publication DataISSN (print): 0036-1429ISSN (online): 1095-7170Publisher: Society for Indu...

Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying graphs. We provide further results on the multipartite separability of Laplacian matrices of graphs. In particular, we identify complete bipartite graphs wh...

We study the spectral convergence of graph Laplacians to Laplace-Beltrami operator when kernelized affinity matrix is constructed from N random samples on a d-dimensional manifold in an ambient Euclidean space. By analyzing Dirichlet form and constructing candidate approximate eigenfunctions via convolution with heat kernel, we prove eigen-convergence rates as increases. The best eigenvalue rat...