Computing automorphisms and canonical labellings of graphs

  • Brendan D. McKay
Contributed Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 686)


A new algorithm is presented for the related problems of canonically labelling a graph or digraph and of finding its automorphism group. The automorphism group is found in the form of a set of less than n generators, where n is the number of vertices. An implementation is reported which is sufficiently conserving of time and space for it to be useful for graphs with over a thousand vertices.


Automorphism Group Search Tree Graph Isomorphism Steiner Triple System Circulant Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Behzad and G. Chartrand, Introduction to the theory of graphs, Allyn and Bacon, Boston (1971).zbMATHGoogle Scholar
  2. [2]
    D.G. Corneil, Graph Isomorphism, Ph.D. Thesis, Univ. of Toronto (1968).Google Scholar
  3. [3]
    B.D. McKay, Backtrack programming and the graph isomorphism problem, M.Sc. Thesis, Univ. of Melbourne (1976).Google Scholar
  4. [4]
    B.D. McKay, "Backtrack programming and isomorph rejection on ordered subsets", to appear in Proc. 5th Australian Conf. on Combin. Math. (1976).Google Scholar
  5. [5]
    R. Parris, The coding problem for graphs, M.Sc. Thesis, Univ. of West Indies (1968).Google Scholar
  6. [6]
    J.P. Steen, "Principle d'un algorithme de recherche d'un isomorphisme entre deux graphes", RIRO, R-3, 3 (1969), 51–69.MathSciNetzbMATHGoogle Scholar
  7. [7]
    H. Wielandt, Finite permutation groups, Academic Press, New York and London (1964).zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Brendan D. McKay
    • 1
  1. 1.Department of MathematicsUniversity of MelbourneParkvilleAustralia

Personalised recommendations