Nodal Domain Theorems and Bipartite Subgraphs

Türker Biyikoglu, Josef Leydold, Peter F. Stadler

Publication: Working/Discussion PaperWU Working Paper

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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. (author's abstract)

Publication series

SeriesPreprint Series / Department of Applied Statistics and Data Processing
Number55

WU Working Paper Series

  • Preprint Series / Department of Applied Statistics and Data Processing

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