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Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix
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Orientador(es)
Resumo(s)
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.
Descrição
Research supported in part by Fundação para a Ciência e a Tecnologia, Portugal, through the research grant SFRH/BD/899/2000. Part of the research was done while visiting the College of William and Mary.
Palavras-chave
Eigenvalues Multiplicity Symmetric matrix Tree Vertex degrees