Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: the case of generalized stars and double generalized stars

Charles R. Johnson, António Leal-Duarte, Carlos Manuel Saiago

Research output: Contribution to journalConference article

34 Citations (Scopus)
1 Downloads (Pure)

Abstract

We characterize the possible lists of orderedmultiplicities among matrices whose graph is a generalized star (a tree in which atmost one vertex has degree greater than 2) or a double generalized star. Here, the inverse eigenvalue problem (IEP) for symmetric matrices whose graph is a generalized star is settled. The answer is consistent with a conjecture that determination of the possible orderedmultiplicities is equivalent to the IEP for a given tree. Moreover, a key spectral feature of the IEP in the case of generalized stars is shown to characterize them among trees.
Original languageEnglish
Pages (from-to)311-330
Number of pages20
JournalLinear Algebra and Its Applications
Volume373
Issue numberSuppl.
DOIs
Publication statusPublished - 1 Nov 2003
EventConference on Combinatorial Matrix Theory - Pohang, Korea, Republic of
Duration: 14 Jan 200217 Jan 2002

Keywords

  • Hermitian matrices
  • Eigenvalues
  • Multiplicities
  • Trees
  • Inverse eigenvalue problems

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