Geodesic
Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix
The electronic journal of linear algebra, Tome 9 (2002), pp. 27-31.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The maximum multiplicity among eigenvalues of matrices with a given graph cannot generally be expressed in terms of the degrees of the vertices (even when the graph is a tree). Given are best possible lower and upper bounds, and characterization of the cases of equality in these bounds. A by-product is a sequential algorithm to calculate the exact maximum multiplicity by simple counting.
Classification : 15A18, 15A57, 05C50, 05C05, 05C07
Keywords: eigenvalues, multiplicity, symmetric matrix, tree, vertex degrees 
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     title = {Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix},
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Johnson, Charles R.; Saiago, Carlos M. Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix. The electronic journal of linear algebra, Tome 9 (2002), pp. 27-31. http://geodesic.mathdoc.fr/item/ELA_2002__9__a21/