Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Académie Serbe des Sciences et des Arts, Beograd

Vol. CXXVII, No. 28, pp. 1-6 (2003)

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Some properties of Laplacian eigenvectors

I. Gutman

Abstract: 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)

Classification (MSC2000): 05C50

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Electronic version published on: 17 Dec 2003. This page was last modified: 17 Dec 2003.

© 2003 Mathematical Institute of the Serbian Academy of Science and Arts
© 2003 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition