The Kronecker product and local computations in graphs

  • Anne Bottreau
  • Yves Métivier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1059)


This paper is concerned with the Kronecker product, and with the applications of some properties to the delimitation of the power of local computations on connected graphs.


Cut-edge Cut-vertex k-covering Local computations on graphs Minor Planar Subgraph The Kronecker product 


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  1. 1.
    D. Angluin. Local and global properties in networks of processors. In 12th STOC, pages 82–93, 1980.Google Scholar
  2. 2.
    D. Angluin and A. Gardiner. Finite common coverings of pairs of regular graphs. J. Combinatorial Theory Ser. B, 30:184–187, 1981.Google Scholar
  3. 3.
    C. Berge. Graphes. Gauthier Villars, 1983.Google Scholar
  4. 4.
    B. Courcelle and Y. Métivier. Coverings and minors: Application to local computations in graphs. Europ. J. Combinatorics, 15:127–138, 1994.Google Scholar
  5. 5.
    W. Dörfler. Zum Kroneckerproduct von endlichen Graphen. Glasnik Matematicki Tom 6, 26(2):217–229, 1971.Google Scholar
  6. 6.
    M. Farzan and D.A. Waller. Kronecker products and local joins of graphs. Can. J. Math., XXIX(2):255–269, 1977.Google Scholar
  7. 7.
    M.J. Fisher, N.A. Lynch, and M. Merritt. Easy impossibility proofs for distributed consensus problems. Jour Distributed Computing, 1:26–39, 1986.Google Scholar
  8. 8.
    A. Gibbons. Algorithmic graph theory. Cambridge University Press, 1985.Google Scholar
  9. 9.
    J.L. Gross and T.W. Tucker. Topological graph theory. Wiley interscience, 1987.Google Scholar
  10. 10.
    I. Litovsky and Y. Métivier. Computing with graph rewriting systems with priorities. Theoretical Computer Science, 115:191–224, 1993.Google Scholar
  11. 11.
    I. Litovsky, Y. Métivier, and E. Sopena. Different local controls for graph relabelling systems. Math. Systems Theory, 28:41–65, 1995.Google Scholar
  12. 12.
    I. Litovsky, Y. Métivier, and W. Zielonka. On the recognition of families of graphs with local computations. Information and Computation, 118(1):110–119, April 1995.Google Scholar
  13. 13.
    D.J. Miller. The categorical product of graphs. Can. J. Math., 20:1511–1521, 1968.Google Scholar
  14. 14.
    D.A. Waller. Double covers of graphs. Bull. Austral. Math. Soc., 14:233–248, 1976.Google Scholar
  15. 15.
    P.M. Weichsel. The Kronecker product of graphs. Proc. Amer. Math. Soc., 8:47–52, 1962.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Anne Bottreau
    • 1
  • Yves Métivier
    • 1
  1. 1.Laboratoire Bordelais de Recherche en InformatiqueURA CNRS 1304Talence CedexFrance

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