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Construction Techniques for Digraphs with Minimum Diameter

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Book cover Combinatorial Algorithms (IWOCA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8288))

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Abstract

We consider the so-called order/degree problem, that is, to determine the smallest diameter of a digraph given order and maximum out-degree. There is no general efficient algorithm known for the construction of such optimal digraphs but various construction techniques for digraphs with minimum diameter have been proposed. In this paper, we survey the known techniques.

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References

  1. Baskoro, E.T., Branković, L., Miller, M., Plesník, J., Ryan, J., Siráň, J.: Large digraphs with small diameter: A voltage assignment approach. JCMCC 24, 161–176 (1997)

    MATH  Google Scholar 

  2. Bridges, W.G., Toueg, S.: On the impossibility of directed Moore graphs. J. Combinatorial Theory Series B29, 339–341 (1980)

    Article  MathSciNet  Google Scholar 

  3. Fiol, M.A., Llado, A.S.: The partial line digraph technique in the design of large interconnection networks. IEEE Trans. on Computers 41(7), 848–857 (1992)

    Article  MathSciNet  Google Scholar 

  4. Fiol, M.A., Llado, A.S., Villar, J.L.: Digraphs on alphabets and the (d,N) digraph problem. Ars Combinatoria 25C, 105–122 (1988)

    MathSciNet  MATH  Google Scholar 

  5. Fiol, M.A., Yebra, J.L.A., Alegre, I.: Line digraph iterations and the (d,k) digraph problem. IEEE Transactions on Computers C-33, 400–403 (1984)

    Article  Google Scholar 

  6. Imase, M., Itoh, M.: Design to minimize a diameter on building block network. IEEE Trans. on Computers C-30, 439–442 (1981)

    Article  MathSciNet  Google Scholar 

  7. Imase, M., Itoh, M.: A design for directed graphs with minimum diameter. IEEE Trans. on Computers C-32, 782–784 (1983)

    Article  Google Scholar 

  8. Miller, M., Fris, I.: Minimum diameter of diregular digraphs of degree 2. Computer Journal 31, 71–75 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  9. Miller, M.: On the monotonicity of minimum diameter with respect to order and maximum out-degree. In: Du, D.-Z., Eades, P., Sharma, A.K., Lin, X., Estivill-Castro, V. (eds.) COCOON 2000. LNCS, vol. 1858, pp. 193–201. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  10. Plesník, J., Znám, Š.: Strongly geodetic directed graphs. In: Acta F. R. N. Univ. Comen. - Mathematica XXIX, pp. 29–34 (1974)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematical and Physical Sciences, University of Newcastle, Australia

    Mirka Miller

  2. Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic

    Mirka Miller

  3. Department of Informatics, King’s College London, United Kingdom

    Mirka Miller

  4. Department of Mathematics, ITB Bandung, Indonesia

    Mirka Miller & Edy Tri Baskoro

  5. School of Information Systems, University of Jember, Indonesia

    Slamin

  6. School of Electrical Engineering and Computer Science, University of Newcastle, Australia

    Joe Ryan & Edy Tri Baskoro

Authors
  1. Mirka Miller
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  2. Slamin
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  3. Joe Ryan
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  4. Edy Tri Baskoro
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Editor information

Editors and Affiliations

  1. UFR des Sciences et Techniques, LITIS, Université de Rouen, 76821, EA 4180, Mont Saint Aignan Cedex, France

    Thierry Lecroq  & Laurent Mouchard  & 

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© 2013 Springer-Verlag Berlin Heidelberg

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Miller, M., Slamin, Ryan, J., Baskoro, E.T. (2013). Construction Techniques for Digraphs with Minimum Diameter. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_28

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  • DOI: https://doi.org/10.1007/978-3-642-45278-9_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45277-2

  • Online ISBN: 978-3-642-45278-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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