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A Note on the Second Largest Eigenvalue of Star-Like Trees

  • Francis K. Bell
  • Slobodan K. Simić
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 430)

Abstract

Star-like trees axe trees homeomorphic to stars. In this paper we identify those star-like trees for which the second largest eigenvalue is extremal — either minimal or maximal — when certain conditions are imposed. We also obtain partial results on the way in which the second largest eigenvalue of a simple class of star-like trees changes under local modifications (graph perturbations). Analogous problems for the largest eigenvalue (known as the index of the graph) have been widely studied in the literature.

Key words and phrases

Graph eigenvalues Second largest eigenvalue Star-like trees Graph modifications 

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Francis K. Bell
    • 1
  • Slobodan K. Simić
    • 2
  1. 1.Department of Mathematics & StatisticsUniversity of StirlingStirlingScotland, United Kingdom
  2. 2.Department of Mathematics, Faculty of Electrical EngineeringUniversity of BelgradeBelgradeYugoslavia

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