Largest Eigenvalue of the Laplacian Matrix: Its Eigenspace and Transitive Orientations
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Largest eigenvalue.pdf
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396.69 KB
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Author(s)
Iriarte Giraldo, Benjamin
Date Issued
November 2016
Journal
SIAM Journal on Discrete Mathematics
Publisher
Society for Industrial and Applied Mathematics
Citation
Iriarte, Benjamin. “Largest Eigenvalue of the Laplacian Matrix: Its Eigenspace and Transitive Orientations.” SIAM Journal on Discrete Mathematics 30, no. 4 (January 2016): 2146–2161 © 2016 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We study the eigenspace with largest eigenvalue of the Laplacian matrix of a simple graph. We find a surprising connection of this space with the theory of modular decomposition of Gallai, whereby eigenvectors can be used to discover modules. In the case of comparability graphs, eigenvectors are used to induce orientations of the graph, and the set of these induced orientations is shown to (recursively) correspond to the full set of transitive orientations.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/15M1008737
