Skip to main content
SpringerLink
Log in

A Structural Approach for Independent Domination of Regular Graphs

  • Original Paper
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

We consider bounds on the minimum cardinality of an independent dominating set in regular graphs with large degree (linear in the number of vertices). Better bounds are obtained for various ranges of the degree. This is done by working with a variant of the clique graph of the complement.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. American Elsevier Publishing Co., Inc, New York (1976)

    MATH  Google Scholar 

  2. Cockayne, E.J., Hedetniemi, S.T.: Disjoint independent dominating sets in graphs. Discrete Math. 15(3), 213–222 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  3. Duckworth, W., Wormald, N.: Linear programming and the worst-case analysis of greedy algorithms on cubic graphs. Electron. J. Combin 17(1), 1–29 (2010). Research Paper 177

  4. Duckworth, W., Wormald, N.C.: On the independent domination number of random regular graphs. Combin. Probab. Comput. 15(4), 513–522 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Erdős, P., Hobbs, A.M., Payan, C.: Disjoint cliques and disjoint maximal independent sets of vertices in graphs. Discrete Math. 42(1), 57–61 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  6. Favaron, O.: Two relations between the parameters of independence and irredundance. Discrete Math. 70(1), 17–20 (1988)

    Article  MathSciNet  Google Scholar 

  7. Goddard, W., Henning, M., Lyle, J., Southey, J.: On the independent domination number of regular graphs. Ann. Comb. 16(4), 719–732 (2012)

  8. Haviland, J.: Upper bounds for independent domination in regular graphs. Discrete Math. 307(21), 2643–2646 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Haviland, J.: Independent dominating sets in regular graphs. J. Comb. Optim. 26(1), 120–126 (2011)

  10. Kostochka, A.V.: The independent domination number of a cubic \(3\)-connected graph can be much larger than its domination number. Gr. Combin. 9(3), 235–237 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lam, P.C.B., Shiu, W.C., Sun, L.: On independent domination number of regular graphs. Discrete Math. 202(1–3), 135–144 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Payan, C.: Sur une classe de problèmes de couverture. C. R. Acad. Sci. Paris Sér. A 278, 233–235 (1974)

    MathSciNet  MATH  Google Scholar 

  13. Payan, C.: Coverings by minimal transversals. Discrete Math. 23(3), 273–277 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  14. Rabern, L.: On hitting all maximum cliques with an independent set. J. Gr. Theor. 66(1), 32–37 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. Rosenfeld, M.: Independent sets in regular graphs. Isr. J. Math. 2, 262–272 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wolk, E.S.: A note on “the comparability graph of a tree”. Proc. Am. Math. Soc. 16, 17–20 (1965)

    MathSciNet  MATH  Google Scholar 

  17. Zito, M.: Greedy algorithms for minimisation problems in random regular graphs. In: Algorithms–ESA 2001 (Århus). Lecture Notes in Computer Science, vol. 2161, pp. 524–536. Springer, Berlin (2001)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS, USA

    Jeremy Lyle

Authors
  1. Jeremy Lyle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeremy Lyle.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lyle, J. A Structural Approach for Independent Domination of Regular Graphs. Graphs and Combinatorics 31, 1567–1588 (2015). https://doi.org/10.1007/s00373-014-1454-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-014-1454-9

Keywords

Mathematics Subject Classification (2010)

Search

Navigation