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Trees

  • Andries E. Brouwer
  • Willem H. Haemers
Chapter
  • 3.3k Downloads
Part of the Universitext book series (UTX)

Abstract

Trees have a simpler structure than general graphs, and we can prove stronger results. For example, interlacing tells us that the multiplicity of an eigenvalue decreases by at most one when a vertex is removed. For trees Godsil’s lemma gives the same conclusion also when a path is removed.

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Copyright information

© Andries E. Brouwer and Willem H. Haemers 2012

Authors and Affiliations

  • Andries E. Brouwer
    • 1
  • Willem H. Haemers
    • 2
  1. 1.Department of MathematicsEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Department of Econometrics and Operations ResearchTilburg UniversityTilburgThe Netherlands

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