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MiS Preprint

Nodal Domain Theorems and Bipartite Subgraphs

Türker Biyikoglu, Josef Leydold and Peter F. Stadler


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.

MSC Codes:
05C50, 05C22, 05C83
graph laplacian, nodal domain theorem, eigenvectors, bipartite graphs

Related publications

2005 Journal Open Access
Josef Leydold, Peter F. Stadler and Türker Biyikoglu

Nodal Domain Theorems and Bipartite Subgraphs

In: The electronic journal of linear algebra, 13 (2005), pp. 344-351