Perron-Frobenius type results and discrete versions of nodal domain theorems

Art M. Duval, Victor Reiner

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We prove discrete versions of nodal domain theorems; in particular, an eigenvector corresponding to the sth smallest eigenvalue of a graph Laplacian has at most s nodal domains. We compare our results to those of Courant and Pleijel on nodal domains of continuous Laplacians, and to those of Fiedler on non-negative regions of graph Laplacians.

Original languageEnglish (US)
Pages (from-to)259-268
Number of pages10
JournalLinear Algebra and Its Applications
Issue number1-3
StatePublished - Jun 15 1999

Bibliographical note

Funding Information:
*Corresponding author. E-mail: 1 E-mail: 2 Partially supported by a Sloan Foundation Fellowship.


  • Graph Laplacian
  • Nodal domain


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