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A Characterization of Cubic Graphs with Paired-Domination Number Three-Fifths Their Order

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Abstract

A paired-dominating set of a graph is a dominating set of vertices whose induced subgraph has a perfect matching, while the paired-domination number is the minimum cardinality of a paired-dominating set in the graph. Recently, Chen et al. (Acta Math Sci Ser A Chin Ed 27(1):166–170, 2007) proved that a cubic graph has paired-domination number at most three-fifths the number of vertices in the graph. In this paper, we show that the Petersen graph is the only connected cubic graph with paired-domination number three-fifths its order.

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References

  1. 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)

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Fitzpatrick S., Hartnell B.: Paired-domination. Discuss. Math. Graph Theory 18, 63–72 (1998)

    MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Computing and Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634, USA

    Wayne Goddard

  2. Department of Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, South Africa

    Michael A. Henning

Authors
  1. Wayne Goddard
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  2. Michael A. Henning
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Correspondence to Wayne Goddard.

Additional information

Research supported in part by the South African National Research Foundation and the University of KwaZulu-Natal.

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Goddard, W., Henning, M.A. A Characterization of Cubic Graphs with Paired-Domination Number Three-Fifths Their Order. Graphs and Combinatorics 25, 675–692 (2009). https://doi.org/10.1007/s00373-010-0884-2

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  • DOI: https://doi.org/10.1007/s00373-010-0884-2

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