Largest Eigenvalue of the Laplacian Matrix: Its Eigenspace and Transitive Orientations
نویسنده
چکیده
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.
منابع مشابه
Largest Eigenvalue of the Laplacian Matrix: Its Eigenspace and Transitive Orientations | SIAM Journal on Discrete Mathematics | Vol. 30, No. 4 | Society for Industrial and Applied Mathematics
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 (rec...
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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 30 شماره
صفحات -
تاریخ انتشار 2016