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The trees for which maximum multiplicity implies the simplicity of other eigenvalues
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Orientador(es)
Resumo(s)
Among those real symmetric matrices whose graph is a given tree $T$, the maximum multiplicity is known to be the path cover number of $T$. An explicit characterization is given for those trees for which whenever the maximum multiplicity is attained, all other multiplicities are $1$.
Descrição
Palavras-chave
Real symmetric matrices Eigenvalues Multiplicities Maximum multiplicity Trees NIM trees Vertex degrees