Largest Eigenvalue of the Laplacian Matrix: Its Eigenspace and Transitive Orientations

Author(s)
Iriarte Giraldo, Benjamin
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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.
Date issued
2016-11
URI
http://hdl.handle.net/1721.1/110183
Department
Massachusetts Institute of Technology. Department of Mathematics
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
ISSN
0895-4801
1095-7146
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