Czechoslovak Mathematical Journal

, Volume 63, Issue 1, pp 73–90 | Cite as

Relations between (κ, τ)-regular sets and star complements

  • Milica AnđelićEmail author
  • Domingos M. Cardoso
  • Slobodan K. Simić


Let G be a finite graph with an eigenvalue µ of multiplicity m. A set X of m vertices in G is called a star set for µ in G if µ is not an eigenvalue of the star complement G\X which is the subgraph of G induced by vertices not in X. A vertex subset of a graph is (κ, τ)-regular if it induces a κ-regular subgraph and every vertex not in the subset has τ neighbors in it. We investigate the graphs having a (κ, τ)-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples.


eigenvalue star complement non-main eigenvalue Hamiltonian graph 

MSC 2010



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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2013

Authors and Affiliations

  • Milica Anđelić
    • 1
    • 2
    Email author
  • Domingos M. Cardoso
    • 1
  • Slobodan K. Simić
    • 3
  1. 1.University of AveiroAveiroPortugal
  2. 2.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia
  3. 3.Mathematical Institute SANUBelgradeSerbia

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