Journal of Mathematical Sciences

, Volume 182, Issue 2, pp 159–163 | Cite as

On induced matchings as star complements in regular graphs

  • P. Rowlinson


We determine all the finite regular graphs which have an induced matching or a cocktail party graph as a star complement.


Adjacency Matrix Regular Graph Complete Bipartite Graph Petersen Graph Graph Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin (1989).MATHGoogle Scholar
  2. 2.
    F. C. Bussemaker, D. Cvetković, and J. J. Seidel, Graphs Related to Exceptional Root Systems, T. H. Report 76-WSK-05, Technological University of Eindhoven (1976).Google Scholar
  3. 3.
    D. M. Cardoso and P. Rama, “Equitable bipartitions of graphs and related results,” J. Math. Sci., 120, 869–880 (2004).MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    D. Cvetković, P. Rowlinson, and S. K. Simić, Spectral Generalizations of Line Graphs, Cambridge Univ. Press, Cambridge (2004).MATHCrossRefGoogle Scholar
  5. 5.
    D. Cvetković, P. Rowlinson, and S. K. Simić, An Introduction to the Theory of Graph Spectra, Cambridge Univ. Press, Cambridge (2009).Google Scholar
  6. 6.
    A. Neumaier, “Regular sets and quasi-symmetric 2-designs,” in: Lect. Notes Math., 969, Springer-Verlag, Berlin (1982), pp. 258–275.Google Scholar
  7. 7.
    P. Rowlinson, “Star partitions and regularity in graphs,” Linear Algebra Appl. 226-228, 247–265 (1995).MathSciNetCrossRefGoogle Scholar
  8. 8.
    P. Rowlinson, “The main eigenvalues of a graph: a survey,” Appl. Anal. Discr. Math. 1, 455–471 (2007).CrossRefGoogle Scholar
  9. 9.
    P. Rowlinson and B. Tayfeh-Rezaie, “Star complements in regular graphs: old and new results,” Linear Algebra Appl., 432, 2230–2242 (2010).MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    D. Stevanović (ed.), “Research problems from the Aveiro workshop on graph spectra,” Linear Algebra Appl. 423, 172–181 (2007).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Mathematics and Statistics Group, Department of Computing Science and MathematicsUniversity of StirlingScotlandUK

Personalised recommendations