We deal with the clustering problem in a metric graph. We look for two clusters, and to this end, we study the first nonzero eigenvalue of the p Laplacian on a quantum graph with Newmann or Kirchoff boundary conditions on ...

© 2018 Elsevier Inc.Let G be an undirected simple graph. The signless Laplacian spread of G is defined as the maximum distance of pairs of its signless Laplacian eigenvalues. This paper establishes some new bounds, both ...

Seeded segmentation methods have gained a lot of attention due to their good performance in fragmenting complex images, easy usability and synergism with graph-based representations. These methods usually rely on sophisticated ...

The recently introduced concept of resolvent energy of a graph [6,7] is based on the adjacency matrix. We now consider the analogous resolvent energies based on the Laplacian and signless Laplacian matrices, and determine ...

The parameter σ(G) of a graph G stands for the number of Laplacian eigenvalues greater than or equal to the average degree of G. In this work, we address the problem of characterizing those graphs G having σ(G) = 1. Our ...

We study the first eigenvalue of the p- Laplacian (with 1 < p< ∞) on a quantum graph with Dirichlet or Kirchoff boundary conditions on the nodes. We find lower and upper bounds for this eigenvalue when we prescribe the ...

We introduce two notions of convexity for an infinite regular tree. For these two notions we show that given a continuous boundary datum there exists a unique convex envelope on the tree and characterize the equation that ...