10 citations · 34 across the 11 of their papers we have counts for
14 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…
Mitigating an epidemic on a geographic network using vaccination
Mohamad Badaoui, Jean-Guy Caputo, Gustavo Cruz-Pacheco +1
We consider a mathematical model describing the propagation of an epidemic on a geographical network. The size of the outbreak is governed by the initial growth rate of the disease…
Analysis of trophic networks: an optimisation approach
Jean-Guy Caputo, Valerie Girardin, Arnaud Knippel +3
We introduce a methodology to study the possible matter flows of an ecosystem defined by observational biomass data and realistic biological constraints. The flows belong to a poly…
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…
Epidemic model on a network: analysis and applications to COVID-19
F. Bustamante-Castaneda, J. -G. Caputo, G. Cruz-Pacheco +2
We analyze an epidemic model on a network consisting of susceptible-infected-recovered equations at the nodes coupled by diffusion using a graph Laplacian. We introduce an epidemic…
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…
Localized solutions of nonlinear network wave equations
J. G. Caputo, I. Khames, A. Knippel +1
We study localized solutions for the nonlinear graph wave equation on finite arbitrary networks. Assuming a large amplitude localized initial condition on one node of the graph, we…
Inverse source problem in a forced network
J. G. Caputo, A. Hamdi, A. Knippel
We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of…
Periodic orbits in nonlinear wave equations on networks
Jean-Guy Caputo, Imene Khames, Arnaud Knippel +1
We consider a cubic nonlinear wave equation on a network and show that inspecting the normal modes of the graph, we can immediately identify which ones extend into nonlinear period…
On the polyhedron of the K-partitioning problem with representative variables
Zacharie Ales, Arnaud Knippel, Alexandre Pauchet
The K-partitioning problem consists of partitioning the vertices of a graph in K sets so as to minimize a function of the edge weights. We introduce a linear mixed integer formulat…
Oscillations of simple networks
Jean-Guy Caputo, Arnaud Knippel, Elie Simo
To describe the flow of a miscible quantity on a network, we introduce the graph wave equation where the standard continuous Laplacian is replaced by the graph Laplacian. This is a…