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On the Domination Numbers of Generalized de Bruijn Digraphs and Generalized Kautz Digraphs

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Computing and Combinatorics (COCOON 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2108))

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Abstract

This work deals with the domination numbers of generalized de Bruijn digraphs and generalized Kautz digraphs. Dominating sets for digraphs are not familiar compared with dominating set for undirected graphs. Whereas dominating sets for digraphs have more applications than undirected graphs. We construct dominating sets of generalized de Bruijn digraphs under some conditions. We investigate consecutive minimum dominating set of the generalized de Bruijn digraphs. For generalized Kautz digraphs, there is a consecutive minimum dominating set that is a minimum dominating set.

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References

  1. Allan, R.B., Laskar, R.: On domination and independent domination number of a graph. Discrete. Math. 23 (1978) 73–76

    Article  MATH  MathSciNet  Google Scholar 

  2. Barkauskas, A.E., Host, L.H.: Finding efficient dominating sets in oriented graphs. Congr. Numer. 98 (1993) 27–32

    MATH  MathSciNet  Google Scholar 

  3. Bar-Yehuda, R., Vishkin, U.: Complexity of finding k-path-free dominating sets in graphs. Info. Process. Letter 14 (1982) 228–232

    Article  MATH  MathSciNet  Google Scholar 

  4. Berge, C., Rao, A.R.: A combinatorial problem in logic. Discrete. Math. 17 (1977) 23–26

    Article  MATH  MathSciNet  Google Scholar 

  5. Bermond, J.-C. Peyrat, C.: De Bruijn and Kautz networks: a competitor for the hypercube ?. Hypercube and Distributed Computers (F. André and J.P. Verjus, Eds.). Elsevier North-Holland, Amsterdam, 1989

    Google Scholar 

  6. Chaty, G., Szwarcfiter, J.L.: Enumerating the kernels of a directed graph with no odd circuits. Info. Proc. Letter 51 (1994) 149–153

    Article  MATH  MathSciNet  Google Scholar 

  7. Duchet, P., Meyniel, H.: Kernels in directed graphs: a poison game. Discrete. Math. 115 (1993) 273–276

    Article  MATH  MathSciNet  Google Scholar 

  8. Fisher, D., Lundgren, J.R., Merz, S.K., Reid, K.B.: Domination graphs of tournaments and digraphs. Congr. Numer. 108 (1995) 97–107

    MATH  MathSciNet  Google Scholar 

  9. Fraenkel, A.S., Yesha, Y.: Complexity of problems in games,graphs, and algebraic equations. Discrete. Appl. Math. 1 (1979) 15–30

    Article  MATH  MathSciNet  Google Scholar 

  10. Ghoshal, J., Laskar, R., Pillone, D.: Topics on domination in directed graphs. Domination in graphs (T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Eds.). Marcel Dekker, New York, 1998, 401–437

    Google Scholar 

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

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  14. Megiddo, N., Vishkin, U.: On finding a minimum dominating set in a tournament. Theor. Comp. Sci. 61 (1988) 307–316

    Article  MathSciNet  MATH  Google Scholar 

  15. Reddy, S.M., Pradhan, D.K., Kuhl, J.: Directed graphs with minimal diameter and maximum node connectivity. School of Engineering Oakland Univ. Tech. Report, 1980

    Google Scholar 

  16. von Neumann J., Morgenstern, O.: Theory of Games and Economic Behaviour. Princeton University Press, Princeton, 1944.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Gunma University, Gunma, 376-8515, Japan

    Yosuke Kikuchi & Yukio Shibata

Authors
  1. Yosuke Kikuchi
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  2. Yukio Shibata
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Massachusetts, One University Avenue, Lowell, MA, 01854, USA

    Jie Wang

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© 2001 Springer-Verlag Berlin Heidelberg

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Kikuchi, Y., Shibata, Y. (2001). On the Domination Numbers of Generalized de Bruijn Digraphs and Generalized Kautz Digraphs. In: Wang, J. (eds) Computing and Combinatorics. COCOON 2001. Lecture Notes in Computer Science, vol 2108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44679-6_45

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  • DOI: https://doi.org/10.1007/3-540-44679-6_45

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42494-9

  • Online ISBN: 978-3-540-44679-8

  • eBook Packages: Springer Book Archive

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