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MiS Preprint
73/2005
Nodal Domain Theorems and Bipartite Subgraphs
Türker Biyikoglu, Josef Leydold and Peter F. Stadler
Abstract
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.
