zbMATH — the first resource for mathematics

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.

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A18 Eigenvalues, singular values, and eigenvectors
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.