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Large eigenvalues of the Laplacian. (English) Zbl 0714.05039
Summary: Let G be a simple graph on n vertices and let \(L=L(G)\) be the Laplacian matrix of G corresponding to some ordering of the vertices. It is known that \(\lambda\leq n\) for any eigenvalue \(\lambda\) of L. In this note we characterize when N is an eigenvalue of L with multiplicity m.

MSC:
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A18 Eigenvalues, singular values, and eigenvectors
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References:
[1] Fiedler M., Czech. Math. J. 98 pp 298– (1973)
[2] Grone R., Czech. Math. J 112 pp 660– (1987)
[3] DOI: 10.1002/andp.18471481202
[4] DOI: 10.1080/03081088708817827
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