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

✍ Scribed by Art M. Duval; Victor Reiner

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 98 KB
Volume: 294
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(99)00090-7

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✦ Synopsis

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.