Publications - Published papers
Please find below publications of our group. Currently, we list 565 papers. Some of the publications are in collaboration with the group of Sonja Prohaska and are also listed in the publication list for her individual group. Access to published papers (
) is restricted to our local network and chosen collaborators.
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) is restricted to our local network and chosen collaborators.
If you have problems accessing electronic information, please let us know:©NOTICE: All papers are copyrighted by the authors; If you would like to use all or a portion of any paper, please contact the author.
Nodal Domain Theorems and Bipartite Subgraphs
Türker Biyikoglu, Josef Leydold, Peter F. Stadler
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Status: Published
Elec.J.Lin.Alg. 13: 344-351 (2005)
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.
Keywords
Graph Laplacian, Nodal Domain Theorem, Eigenvectors, Bipartite Graphs
Note
AMS: 05C50 Graphs and matrices, 05C22 Signed, gain and biased graphs, 05C83 Graph minors.