371 citations · 392 across the 10 of their papers we have counts for
11 papers
Graph transformations and eigenvectors of the Laplacian, signless Laplacian and Adjacency matrices
Jean-Guy Caputo, Leonardo de Lima, Arnaud Knippel
We study graph transformations and their effects on the eigenvectors of three fundamental graph matrices: the adjacency matrix , the signless Laplacian , and the Laplacian $L…
On some classes of bivalent and trivalent planar graphs
Jorge Alencar, Jean-Guy Caputo, Leonardo de Lima +1
A graph is called bivalent or trivalent if there exists an eigenvector of the graph Laplacian composed from {-1,1} or {-1,0,1}, respectively. These bivalent and trivalent eigenvect…
Eigenvectors of graph Laplacians: a landscape
J. -G. Caputo, A. Knippel
We review the properties of eigenvectors for the graph Laplacian matrix, aiming at predicting a specific eigenvalue/vector from the geometry of the graph. After considering classic…
Spectra of chains connected to complete graphs
J. -G. Caputo, G. Cruz-Pacheco, A. Knippel +1
We characterize the spectrum of the Laplacian of graphs composed of one or two finite or infinite chains connected to a complete graph. We show the existence of localized eigenvect…
Liouville type theorems, a priori estimates and existence of solutions for critical order Hardy-Hénon equations in
Wenxiong Chen, Wei Dai, Guolin Qin
In this paper, we consider the critical order Hardy-Hénon equations \begin{equation*} (-Δ)^{\frac{n}{2}}u(x)=\frac{u^{p}(x)}{|x|^{a}}, \,\,\,\,\,\,\,\,\,\,\, x \, \in \,\, \mathbb{…
On graph Laplacian eigenvectors with components in {-1,0,1}
J-G. Caputo, I. Khames, A. Knippel
We characterize all graphs for which there are eigenvectors of the graph Laplacian having all their components in {-1,+1} or {-1,0,+ 1}. Graphs having eigenvectors with components…