Planarity Criteria for Metric Graphs
Abstract
Abstract The Colin de Verdière parameter is a number assigned to discrete graphs which equals the maximal multiplicity of the second eigenvalue of a certain family of Laplacian matrices related to the graph. In this paper it is shown that the Colin de Verdière parameter can be obtained in the setting of metric graphs by looking at the maximal multiplicity of the second eigenvalue for Laplacians on metric graphs with delta couplings at the vertices. Two different families of Laplacians, as well as a family of Schrödinger operators, all leading to the Colin de Verdière number are presented.
Fields of Study & Subjects
Graph theory and applications
Spectral Theory in Mathematical Physics
Markov Chains and Monte Carlo Methods
Publication details
- Journal / source
- Integral Equations and Operator Theory
- Volume
- 98
- Issue
- 4
- Publication date
- 11 September 2026
- Language
- EN