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Zbl 1015.05051
Hagos, Elias M.
Some results on graph spectra. (English)
[J] Linear Algebra Appl. 356, No.1-3, 103-111 (2002). ISSN 0024-3795

Summary: This paper presents a variety of results on graph spectra. The number of main eigenvalues of a graph is shown to be equal to the rank of an associated matrix. We establish a condition for a graph to have exactly two main eigenvalues and then show how to evaluate them and their associated eigenvectors. It is shown that the main eigenvalues and corresponding eigenvectors of a graph determine those of its complement. We generalize to any eigenvalue a condition for $0$ and $-1$ to be eigenvalues of a graph and its complement, respectively. Finally, we generalize to non-simple eigenvalues a result on the components of an eigenvector associated with a simple eigenvalue.

MSC 2000:: *05C50 Graphs and matrices

Keywords: main eigenvalues

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Zentralblatt MATH Berlin [Germany]