The trees for which maximum multiplicity implies the simplicity of other eigenvalues

Charles R. Johnson, Carlos Manuel Saiago

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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Abstract

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 $1$.
Original languageEnglish
Pages (from-to)3130-3135
Number of pages6
JournalDiscrete Mathematics
Volume306
Issue number23(SI)
DOIs
Publication statusPublished - 6 Dec 2006

Keywords

  • Real symmetric matrices
  • Eigenvalues
  • Multiplicities
  • Maximum multiplicity
  • Trees
  • NIM trees
  • Vertex degrees

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