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Paired-Domination in Claw-Free Graphs

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Abstract

A paired-dominating set of a graph G is a dominating set of vertices whose induced subgraph has a perfect matching, while the paired-domination number, denoted by γ pr (G), is the minimum cardinality of a paired-dominating set in G. In this paper we investigate the paired-domination number in claw-free graphs. Specifically, we show that γ pr (G) ≤ (3n − 1)/5 if G is a connected claw-free graph of order n with minimum degree at least three and that this bound is sharp.

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References

  1. Chen L., Lu C.H., Zeng Z.B.: Labelling algorithms for paired-domination problems in block and interval graphs. J. Combin. Optim. 19, 457–470 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen X.G., Sun L., Xing H.M.: Paired-domination numbers of cubic graphs (Chinese). Acta Math. Sci. Ser. A Chin. Ed. 27, 166–170 (2007)

    MathSciNet  MATH  Google Scholar 

  3. Chen X.G., Wai C.S., Wai H.C.: Upper bounds on the paired-domination number. Appl. Math. Lett. 21, 1194–1198 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cheng T.C.E., Kang L.Y., Ng C.T.: Paired domination on interval and circular-arc graphs. Discrete Appl. Math. 155, 2077–2086 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dorbec P., Henning M.A.: Upper paired-domination in claw-free graphs. J. Combin. Optim. 22, 235–251 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dorbec P., Gravier S., Henning M.A.: Paired-domination in generalized claw-free graphs. J. Combin. Optim. 14, 1–7 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Favaron O., Henning M.A.: Paired domination in claw-free cubic graphs. Graphs Combin. 20, 447–456 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Goddard W., Henning M.A.: A characterization of cubic graphs with paired-domination number three-fifths their order. Graphs Combin. 25, 675–692 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Haynes T.W., Hedetniemi S.T., Slater P.J.: Fundamentals of Domination in Graphs. Marcel Dekker, New York (1998)

    MATH  Google Scholar 

  10. Haynes T.W., Hedetniemi S.T., Slater P.J.: Domination in Graphs: Advanced Topics. Marcel Dekker, New York (1998)

    MATH  Google Scholar 

  11. Haynes T.W., Slater P.J.: Paired-domination in graphs. Networks 32, 199–206 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. Haynes T.W., Slater P.J.: Paired-domination and the paired-domatic number. Congr. Numer. 109, 65–72 (1995)

    MathSciNet  MATH  Google Scholar 

  13. Henning M.A.: Graphs with large paired-domination number. J. Combin. Optim. 13, 61–78 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Henning M.A., Plummer M.D.: Vertices contained in all or in no minimum paired-dominating set of a tree. J. Combin. Optim. 10, 283–294 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Huang S.W., Shan E.F.: A note on the upper bound for the paired-domination number of a graph with minimum degree at least two. Networks 57, 115–116 (2011)

    MathSciNet  MATH  Google Scholar 

  16. Qiao H., Kang L.Y., Cardei M., Du D.Z.: Paired-domination of trees. J. Global Optim. 25, 43–54 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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Author notes

  1. Shenwei Huang

    Present address: School of Computing Science, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Shenwei Huang & Liying Kang

  2. School of Management, Shanghai University, Shanghai, People’s Republic of China

    Erfang Shan

Authors
  1. Shenwei Huang
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  2. Liying Kang
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  3. Erfang Shan
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Corresponding author

Correspondence to Liying Kang.

Additional information

This research was partially supported by the National Nature Science Foundation of China (Nos. 11171207, 10971131, 91130032).

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Huang, S., Kang, L. & Shan, E. Paired-Domination in Claw-Free Graphs. Graphs and Combinatorics 29, 1777–1794 (2013). https://doi.org/10.1007/s00373-012-1224-5

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  • DOI: https://doi.org/10.1007/s00373-012-1224-5

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