Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix

Charles R. Johnson, Carlos Manuel Saiago

Research output: Contribution to journalArticle

16 Citations (Scopus)
4 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)27-31
Number of pages5
JournalElectronic Journal Of Linear Algebra
Volume9
Issue number3
DOIs
Publication statusPublished - Mar 2002

Keywords

  • Eigenvalues
  • Multiplicity
  • Symmetric matrix
  • Tree
  • Vertex degrees

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