Geodesic
Some properties of Laplacian eigenvectors
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 28 (2003) no. 1.

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $G$ be a graph on $n$ vertices, $\bar G$ its complement and $K_n$ the complete graph on $n$ vertices. We show that if $G$ is connected, then any Laplacian eigenvector of $G$ is also a Laplacian eigenvector of $\bar G$ and of $K_n$ . This result holds, with a slight modification, also for disconnected graphs. We establish also some other results, all showing that the structural information contained in the Laplacian eigenvectors is rather limited. An analogy between the theories of Laplacian and ordinary graph spectra is pointed out.
Keywords: Laplacian spectrum, Laplacian matrix, Laplacian eigenvector (of graph), Laplacian eigenvalue (of graph) 
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     author = {I. Gutman},
     title = {Some properties of {Laplacian} eigenvectors},
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     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2003},
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     url = {http://geodesic.mathdoc.fr/item/BASS_2003_28_1_a0/}
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I. Gutman. Some properties of Laplacian eigenvectors. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 28 (2003) no. 1. http://geodesic.mathdoc.fr/item/BASS_2003_28_1_a0/