Some properties of Laplacian eigenvectors. (English) Zbl 1051.05059

Gutman, I.

Bull., Cl. Sci. Math. Nat., Sci. Math. 127, No. 28, 1-6 (2003).

An eigenvector of the Laplacian matrix of a graph \(G\) is called Laplacian eigenvector of \(G\). It is shown that any Laplacian eigenvector of a connected graph \(G\) on \(n\) vertices is also a Laplacian eigenvector of the complement \(\overline G\) and of the complete graph \(K_n\). This means that Laplacian eigenvectors (without specification to which eigenvalues they belong) contain no information on the graph structure.

Reviewer: Dragoš Cvetković (Beograd)

MSC:

05C50

Graphs and linear algebra (matrices, eigenvalues, etc.)

Keywords:

graph spectra; Laplacian matrix; Laplacian eigenvector