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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
##### Keywords:
Laplacian matrix; eigenvalue
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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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