Nodal domain theorems and bipartite subgraphs
The electronic journal of linear algebra, Tome 13 (2005), pp. 344-351.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The Discrete Nodal Domain Theorem states that an eigenfunction of the k-th largest eigenvalue of a generalized graph Laplacian has at most k (weak) nodal domains. The number of strong nodal domains is shown not to exceed the size of a maximal induced bipartite subgraph and that this bound is sharp for generalized graph Laplacians. Similarly, the number of weak nodal domains is bounded by the size of a maximal bipartite minor.
Classification : 05C50, 05C22, 05C83
Keywords: graph Laplacian, nodal domain theorem, eigenvectors, bipartite graphs
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     title = {Nodal domain theorems and bipartite subgraphs},
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Bıyıkoğlu, Türker; Leydold, Josef; Stadler, Peter F. Nodal domain theorems and bipartite subgraphs. The electronic journal of linear algebra, Tome 13 (2005), pp. 344-351. http://geodesic.mathdoc.fr/item/ELA_2005__13__a4/