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. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing
| Identifer | oai:union.ndltd.org:VIENNA/oai:epub.wu-wien.ac.at:epub-wu-01_9fc |
| Date | January 2005 |
| Creators | Biyikoglu, TĂĽrker, Leydold, Josef, Stadler, Peter F. |
| Publisher | Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business |
| Source Sets | Wirtschaftsuniversität Wien |
| Language | English |
| Detected Language | English |
| Type | Paper, NonPeerReviewed |
| Format | application/pdf |
| Relation | http://epub.wu.ac.at/626/ |
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