Skip to main content
SpringerLink
Log in

Graph isomorphism: A heuristic edge-partitioning-oriented algorithm

Ein heuristischer Algorithmus zum Nachweis der isomorphie von Graphen

  • Published:
Computing Aims and scope Submit manuscript

Abstract

A new algorithm for testing isomorphism on directed and undirected graphs is described. It consists of an 0 (n 5) algorithm for partitioning node and edge sets, plus a heuristic procedure for deriving all the isomorphisms. The partitioning is described by a “connectivity graph” on which a sufficient condition for isomerphism can be tested.

Zusammenfassung

Die Arbeit enthält die Beschreibung eines neuen heuristischen Algorithmus, der überprüft ob zwei Graphen isomorph sind. Der Algorithmus besteht aus zwei Teilen. Der erste Teil, ein 0 (n 5)-Algorithmus, liefert eine Knoten- und Kantenpartition. Der zweite Teil gewinnt aus diesen Partitionen auf Grund heuristischer Überlegungen alle möglichen Isomorphismen. Die Knoten- und Kantenpartitionen werden mit Hilfe eines Connectivity-Graphen beschrieben, an Hand dessen eine hinreichende Bedingung für die Existenz eines Isomorphismus überprüft werden kann.

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.

Similar content being viewed by others

References

  1. Unger, S. H.: GIT — A heuristic program for testing pairs of directed line graphs for isomorphism. Comm. ACM7, 26–34 (1964).

    Google Scholar 

  2. Böhm, C., and A. Santolini: A quasi-decision algorithm for thep-equivalence of two matrices. ICC Bull.3, 57–69 (1964).

    Google Scholar 

  3. Salton, G., and E. H. Sussengurth, Jr.: Some flexible information retrieval systems using structure matching procedure. Proc. AFIPS 1964 SJCC25, pp. 587–598. New York: Spartan Books. 1964.

    Google Scholar 

  4. Sussenguth, E. H., Jr.: A graph-theoretical algorithm for matching chemical structures. J. Chem. Doc.5, 36–43 (1965).

    Google Scholar 

  5. Hopcroft, J., and R. Tarjan: Planarity testing inV logV steps: extended abstract. Proc. IFIP Congress 1971, Booklet TA-2, pp. 18–22 (1971).

    Google Scholar 

  6. Corneil, D. G., and C. C. Gotlieb: An efficient algorithm for graph isomorphism. J. ACM17, 51–64 (1970).

    Google Scholar 

  7. Corneil, D. G.: Graph isomorphism. Tech. Rept. No 18, Dept. of Computer Science, Univ. of Toronto, April 1970.

  8. Morpurgo, R.: Un metodo euristico per la verifica dell'isomorfismo di due grafi semplici non orientati. Calcolo8, 1–31 (1971).

    Google Scholar 

  9. Sirovich, F.: Isomorfismo fra grafi: un algoritmo efficiente per trovare tutti gli isomorfismi. Calcolo8, 301–337 (1971).

    Google Scholar 

  10. Levi, G.: A note on the derivation of maximal common subgraphs of two directed or undirected graphs. Calcolo9, 1–12 (1972).

    Google Scholar 

  11. Grace, D. W.: Computer search for non-isomorphic convex polyhedra. Ph. D. Thesis, Stanford University, 1965.

  12. Goethals, J. M., and J. J. Seidel: Orthogonal matrices with zero diagonal. Canad. J. Math.19, 1001–1010 (1967).

    Google Scholar 

  13. Levi, G.: A heuristic search procedure for testing sugraph isomorphism. (In preparation.)

Download references

Author information

Authors and Affiliations

  1. Istituto di Elaborazione dell'Informazione, Consiglio Nazionale delle Ricerche, Via S. Maria, 46, I-56100, Pisa, Italy

    G. Levi

Authors
  1. G. Levi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

With 10 Figures

Rights and permissions

Reprints and permissions

About this article

Cite this article

Levi, G. Graph isomorphism: A heuristic edge-partitioning-oriented algorithm. Computing 12, 291–313 (1974). https://doi.org/10.1007/BF02253334

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02253334

Keywords

Search

Navigation