Mathematical Notes

, Volume 62, Issue 4, pp 449–456 | Cite as

Generalized de Bruijn graphs

  • F. M. Malyshev
  • V. E. Tarakanov
Article

Abstract

Oriented graphs in which every pair of vertices can be connected by a unique path of given length (not depending on the choice of the pair of vertices) are studied. These graphs are a natural extension of the well-known de Bruijn graphs and retain their most important properties. Some results on the structure of and methods for constructing such graphs are obtained.

Key Words

oriented graphs de Bruijn graphs adjacency matrix simple graphs 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Hall, Jr.,Combinatorial Theory, Toronto (1967).Google Scholar
  2. 2.
    I. J. Good, “Normal recurring decimals,”J. London Math. Soc.,21, 167–169 (1946).MATHMathSciNetGoogle Scholar
  3. 3.
    H. Fredricksen, “A survey of full length nonlinear shift register cycle algorithms,”SIAM Rev.,24, No. 2, 195–221 (1982).MATHMathSciNetGoogle Scholar
  4. 4.
    M. I. Kratko and V. V. Strok, “De Bruijn Sequences With Constraints,” in:Questions of Cybernetics: Combinatorial Analysis and Graph Theory [in Russian], Nauka, Moscow (1980), pp. 80–84.Google Scholar
  5. 5.
    I. V. Shirisheva (I. V. Sherisheva), “On the number of finite automata stabilized by a constant input in a fixed state,”Diskret. Mat. [Discrete Math. Appl.],6, No. 4, 80–86 (1994).Google Scholar
  6. 6.
    F. Harary,Graph Theory, Addison-Wesley, Reading (USA) (1973).Google Scholar
  7. 7.
    C. M. Allow and J. L. Brenner, “Roots and canonical forms for circulant matrices,”Trans. Amer. Math. Soc.,107, 60–76 (1963).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • F. M. Malyshev
    • 1
  • V. E. Tarakanov
    • 1
  1. 1.V. A. Steklov Mathematics InstituteRussian Academy of SciencesRussia

Personalised recommendations