- AutorIn
- Türker Biyikoglu
- Wim Hordijk
- Josef Leydold
- Tomaz Pisanski
- Peter F. Stadler
- Titel
- Graph Laplacians, Nodal Domains, and Hyperplane Arrangements
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa2-321457
- Quellenangabe
- Linear algebra and its applications Erscheinungsort: New York, NY
Verlag: American Elsevier Publ.
Erscheinungsjahr: 2004
Jahrgang: 390
Seiten: 155-174 - Erstveröffentlichung
- 2004
- Abstract (EN)
- Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. Here we investigate their so-called nodal domains, i.e. the connected components of the maximal induced subgraphs of G on which an eigenvector ψ does not change sign. An analogue of Courant's nodal domain theorem provides upper bounds on the number of nodal domains depending on the location of ψ in the spectrum. This bound, however, is not sharp in general. In this contribution we consider the problem of computing minimal and maximal numbers of nodal domains for a particular graph. The class of Boolean Hypercubes is discussed in detail. We find that, despite the simplicity of this graph class, for which complete spectral information is available, the computations are still non-trivial. Nevertheless, we obtained some new results and a number of conjectures.
- Freie Schlagwörter (EN)
- Graph Laplacians, Nodal domains, Hyperplane arrangements
- Klassifikation (DDC)
- 510.72
- Version / Begutachtungsstatus
- publizierte Version / Verlagsversion
- URN Qucosa
- urn:nbn:de:bsz:15-qucosa2-321457
- Veröffentlichungsdatum Qucosa
- 08.11.2018
- Dokumenttyp
- Artikel
- Sprache des Dokumentes
- Englisch