Largest Eigenvalue of the Laplacian Matrix: Its Eigenspace and Transitive Orientations
نویسندگان
چکیده
منابع مشابه
Largest Eigenvalue of the Laplacian Matrix: Its Eigenspace and Transitive Orientations
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...
متن کاملLargest 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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Abstract. Let G be a simple undirected connected graph on n vertices. Suppose that the vertices of G are labelled 1,2, . . . ,n. Let di be the degree of the vertex i. The Randić matrix of G , denoted by R, is the n× n matrix whose (i, j)−entry is 1 √ did j if the vertices i and j are adjacent and 0 otherwise. The normalized Laplacian matrix of G is L = I−R, where I is the n× n identity matrix. ...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2016
ISSN: 0895-4801,1095-7146
DOI: 10.1137/15m1008737