Skip to main content
SpringerLink
Log in

Efficient Minus and Signed Domination in Graphs

  • Conference paper
  • First Online:
Algorithms and Computation (ISAAC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1969))

Included in the following conference series:

Abstract

We show that the efficient minus (resp., signed) domination problem is NP-complete for chordal graphs, chordal bipartite graphs, planar bipartite graphs and planar graphs of maximum degree 4 (resp., for chordal graphs). Based on the forcing property on blocks of vertices and automata theory, we provide a uniform approach to show that in a special class of interval graphs, every graph (resp., every graph with no vertex of odd degree) has an efficient minus (resp., signed) dominating function. Besides, we show that the efficient minus domination problem is equivalent to the efficient domination problem on trees.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D.W. Bange, A.E. Barkauskas, L.H. Host, and P.J. Slater, Generalized dominationand efficient domination in graphs, Discrete Mathematics, 159 (1996) 1–11.

    Article  MATH  MathSciNet  Google Scholar 

  2. D.W. Bange, A. Barkauskas, and P.J. Slater, Efficient dominating sets in graphs,in: R.D. Ringeisen and F.S. Roberts eds., Application of Discrete Mathematics,(SIAM, Philadelphia, PA, 1988) 189–199.

    Google Scholar 

  3. A. Brandstädt, V.B. Le, and J.P. Spinrad, Graph Classes—A Survey, SIAM Monographs on Discrete Mathematics and Applications, Philadelphia, 1999.

    Google Scholar 

  4. G.J. Chang, C. Pandu Rangan, and S.R. Coorg, Weighted independent perfectdomination on cocomparability graphs, Discrete Applied Mathematics, 63 (1995)215–222.

    Article  MATH  MathSciNet  Google Scholar 

  5. M.S. Chang, Weighted domination of cocomparability graphs, Discrete AppliedMathematics, 80 (1997) 135–148.

    MATH  Google Scholar 

  6. M.S. Chang and Y.C. Liu, Polynomial algorithm for the weighted perfect domina-tion problems on chordal graphs and split graphs, Information Processing Letters,48 (1993) 205–210.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. Damaschke, Minus domination in small-degree graphs, in: Proceedings of the24th International Workshop on Graph-Theoretic Concepts in Computer Science,Lecture Notes in Computer Science, 1517 (1998) 17–25.

    Google Scholar 

  8. J. Dunbar, W. Goddar, S. Hedetniemi, A. McRae, and M.A. Henning, The algo-rithmic complexity of minus domination in graphs, Discrete Applied Mathematics,68 (1996) 73–84.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Dunbar, S.T. Hedetniemi, M.A. Henning, and P.J. Slater, Signed domination ingraphs, in: Y. Alari and A. Schwenk, eds., Proc. 7th International Conference onthe Theory and Applications of Graphs, (Wiley, New York, 1995) 311–321.

    Google Scholar 

  10. M.R. Fellows and M.N. Hoover, Perfect domination, Australasian Journal of Com-binatorics, 3 (1991) 141–150.

    MATH  MathSciNet  Google Scholar 

  11. M.R. Garey and D.S. Johnson, Computers and Intractability — A Guide to theTheory of NP-Completeness, San Francisco, Freeman, 1979.

    Google Scholar 

  12. P.C. Gilmore and A.J. Hoffman, A characterization of comparability graphs andof interval graphs, Canadian Journal of Mathematics, 16 (1964) 539–548.

    MATH  MathSciNet  Google Scholar 

  13. M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press,New York, 1980.

    Google Scholar 

  14. J.H. Hattingh, M.A. Henning, and P.J. Slater, The algorithmic complexity of signeddomination in graphs, Australasian Journal of Combinatorics, 12 (1995) 101–112.

    MATH  MathSciNet  Google Scholar 

  15. T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination inGraphs, Marcel Dekker, New York, 1998.

    Google Scholar 

  16. J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, andComputation, Addison-Wesley, Reading, MA, 1979.

    Google Scholar 

  17. Y.D. Liang, C.L. Lu, and C.Y. Tang, Efficient domination on permutation graphsand trapezoid graphs, in: T. Jiang and D.T. Lee, eds., Proc. 3rd Annual Interna-tional Computing and Combinatorics Conference (COCOON’97), Lecture Notesin Computer Science, 1276 (Springer-Verlag, 1997) 232–241.

    Google Scholar 

  18. C.L. Lu, On the Study of Weighted Efficient Domination, PhD Thesis, Departmentof Computer Science, National Tsing Hua University, Taiwan, 1998.

    Google Scholar 

  19. C.C. Yen,Algorithmic Aspects of Perfect Domination, PhD Thesis, Department ofComputer Science, National Tsing Hua University, Taiwan, 1992.

    Google Scholar 

  20. C.C. Yen and R.C.T. Lee, The weighted perfect domination problem and its vari-ants, Discrete Applied Mathematics, 66 (1996) 147–160.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Center for High-Performance Computing, P.O. Box 19-136, 300, Hsinchu, Taiwan, R.O.C

    Chin Lung Lu

  2. Department of Computer Science and Information Engineering, National DongHwa University, Hualien, Taiwan, R.O.C

    Sheng-Lung Peng

  3. Department of Computer Science, National Tsing Hua University, 300, Hsinchu, Taiwan, R.O.C

    Chuan Yi Tang

Authors
  1. Chin Lung Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sheng-Lung Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chuan Yi Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Academia Sinica, Institute of Information Science, 128 Academia Road, Section 2, Nankang, 115, Taipei, Taiwan, R.O.C.

    D. T. Lee

  5. Department of Computer Science and Akamai Technologies, University of Illinois at Urbana Champaign, 500 Technology Square, 02139, Cambridge, MA, USA

    Shang-Hua Teng

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lu, C.L., Peng, SL., Tang, C.Y. (2000). Efficient Minus and Signed Domination in Graphs. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-40996-3_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41255-7

  • Online ISBN: 978-3-540-40996-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation