The electronic journal of linear algebra Verlag: Soc.
Erscheinungsjahr: 2005
Jahrgang: 13 ISSN: 1081-3810 Artikelnummer: 21
Erstveröffentlichung
2005
Abstract (EN)
The Discrete Nodal Domain Theorem states that an eigenfunction of the k-th largest eigenvalue of a generalized graph Laplacian has at most k (weak) nodal domains. We show that the number of strong nodal domains cannot exceed the size of a maximal induced bipartite subgraph and that this bound is sharp for generalized graph Laplacians. Similarly, the number of weak nodal domains is bounded by the size of a maximal bipartite minor.