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

Art M. Duval; Victor Reiner

doi:10.1016/S0024-3795(99)00090-7

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

Art M. Duval, Victor Reiner

School of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	259-268
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	294
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(99)00090-7
State	Published - Jun 15 1999

Bibliographical note

Funding Information:
*Corresponding author. E-mail: reiner@math.umn.edu 1 E-mail: artduval@math.utep.edu 2 Partially supported by a Sloan Foundation Fellowship.

Keywords

Graph Laplacian
Nodal domain

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10.1016/S0024-3795(99)00090-7

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title = "Perron-Frobenius type results and discrete versions of nodal domain theorems",

abstract = "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.",

keywords = "Graph Laplacian, Nodal domain",

author = "Duval, {Art M.} and Victor Reiner",

note = "Funding Information: *Corresponding author. E-mail: reiner@math.umn.edu 1 E-mail: artduval@math.utep.edu 2 Partially supported by a Sloan Foundation Fellowship.",

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AU - Duval, Art M.

AU - Reiner, Victor

N1 - Funding Information: *Corresponding author. E-mail: reiner@math.umn.edu 1 E-mail: artduval@math.utep.edu 2 Partially supported by a Sloan Foundation Fellowship.

PY - 1999/6/15

Y1 - 1999/6/15

N2 - 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.

AB - 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.

KW - Graph Laplacian

KW - Nodal domain

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U2 - 10.1016/S0024-3795(99)00090-7

DO - 10.1016/S0024-3795(99)00090-7

M3 - Article

AN - SCOPUS:0033460530

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VL - 294

SP - 259

EP - 268

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

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

Abstract

Bibliographical note

Keywords

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