Skip to main content
SpringerLink
Log in

Associative products of graphs

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

It is shown that there exist exactly twenty products of graphs defined on the Cartesian product of the vertex sets of the factors where the adjacencies of the vertices only depend on the adjacencies in the factors.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Berge, C.: The Theory of Graphs and Its Applications. London: Methuen. 1962.

    Google Scholar 

  2. Dörfler, W., undW. Imrich: Das lexikographische Produkt gerichteter Graphen. Mh. Math.76, 21–30 (1972).

    Google Scholar 

  3. Čulík, K.: Zur Theorie der Graphen. Časopis Pěst. Mat.83, 133–155 (1958).

    Google Scholar 

  4. Harary F., andG. Wilcox: Boolean operations on graphs. Math. Scand.20, 41–51 (1967).

    Google Scholar 

  5. Imrich, W.: Über das schwache kartesische Produkt von Graphen. J. Comb. Th. Ser. B11, 1–16 (1971).

    Google Scholar 

  6. Lovász, L.: On the cancellation law among finite relational structures. Periodica Math. Hung.1, 145–156 (1971).

    Google Scholar 

  7. McKenzie, R.: Cardinal multiplication of structures with a reflexive relation. Fund. Math.70, 59–101 (1971).

    Google Scholar 

  8. Miller, D. J.: The categorical product of graphs. Canad. J. Math.20, 1511–1521 (1968).

    Google Scholar 

  9. Miller, D. J. Weak Cartesian product of graphs. Colloquium Math.21, 55–74 (1970).

    Google Scholar 

  10. Pultr, A.: Tensor Products on the Category of Graphs. Combinatorial Structures and Their Applications. New York: Gordon and Breach. 1970.

    Google Scholar 

  11. Sabidussi, G.: Graph multiplication. Math. Z.72, 446–457 (1960).

    Google Scholar 

  12. Weichsel, P. M.: The Kronecker product of graphs. Proc. Amer. Math. Soc.13, 47–52 (1962).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Montanuniversität, A-8700, Leoben, Austria

    Wilfried Imrich

  2. IBM Laboratorium Wien, Parkring 10, A-1010, Wien, Austria

    Herbert Izbicki

Authors
  1. Wilfried Imrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Herbert Izbicki
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Prof. N. Hofreiter on his seventieth birthday

Supported by the Canadian National Research Council.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Imrich, W., Izbicki, H. Associative products of graphs. Monatshefte für Mathematik 80, 277–281 (1975). https://doi.org/10.1007/BF01472575

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01472575

Keywords

Search

Navigation