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On Writing Isomorphism Programs

  • William Kocay

Abstract

This is a self-contained exposition on how to write isomorphism programs. It is intended for people who want to write isomorphism programs for combinatorial structures, such as graphs, designs, digraphs, posets, etc.

Keywords

Cell Orbit Leaf Node Adjacency Matrix Search Tree Graph Isomorphism 
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.

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References

  1. [1]
    A. Aho, J. Hoperoft, and J. Ullman, The Design and Analysis of Computer Algorithms, Addison Wesley, Toronto, 1974.zbMATHGoogle Scholar
  2. [2]
    L. Babai, P. Erdös, S.M. Selkow, Random graph isomorphism, SIAM J. of Computing 9 (1980), 628–635.CrossRefzbMATHGoogle Scholar
  3. [3]
    Laszlo Babai and Eugene Luks, Canonical labeling of graphs,Proc. 15th Annual ACM Symp. on Theory of Computing, SIGACT, 1983.Google Scholar
  4. [4]
    J.M. Bennett and J.J. Edwards, A graph isomorphism algorithm using pseudoinverses, preprint, Computer Science Department, University of Sydney.Google Scholar
  5. [5]
    N.L. Biggs and A.T. White, Permutation Groups and Combinatorial Structures, London Math. Soc. Lecture Notes #33, Cambridge Univ. Press, Cambridge, 1979.Google Scholar
  6. [6]
    Bela Bollobas,Graph Theory, an Introductory Course,Springer-Verlag, New York, 1979.Google Scholar
  7. [7]
    Gregory Butler and John Cannon, Computing in permutation and matrix groups I: normal closure, commutator subgroups, series, Mathematics of Computation 39 (1982), 663–670.MathSciNetzbMATHGoogle Scholar
  8. [8]
    G. Butler and C.W.H. Lam, A general backtrack algorithm for the isomorphism problem of combinatorial objects, J. Symbolic Computation 1 (1985), 363–381.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Derek Corneil and Mark Goldberg, A non-factorial algorithm for canonical numbering of a graph, Technical Report #160/82, 1982, Department of Computer Science, University of Toronto.Google Scholar
  10. [10]
    D.G. Corneil and C.C. Gotlieb, An efficient algorithm for graph isomorphism, JACM 17 (1970) 51–64.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    D.G. Corneil and D.G. Kirkpatrick, A theoretical analysis of various heuristics for the graph isomorphism problem, SIAM J. Computing 9 (1982), 281–297.MathSciNetCrossRefGoogle Scholar
  12. [12]
    M. Furst, J.E. Hoperoft, and E. Luks, A subexponential algorithm for trivalent graph isomorphism, 1980, Tech. Rept. 80–426, Dept. of Computer Science, Cornell University.Google Scholar
  13. [13]
    R.M. Karp, Probabilisitic analyisis of a canonical numberiung algorithm for graphs, Proc. Symp. Pure Math. 34 (1979), 365–378.MathSciNetGoogle Scholar
  14. [14]
    Zvi Galil, Christoff M. Hoffmann, Eugene M. Luks, Claus P. Schnorr, and Andreas Weber, An O(n3 log n) deterministic and 0(n3) probabilistic isomorphism test for trivalent graphs, Proc. 23rd IEEE Symp. on the Foundations of Comp. Sci., N.Y., 1982, pp. 118–125.Google Scholar
  15. [15]
    S.J. Gismondi and E.R. Swart, A polynomial-time procedure for resolving the graph isomorphism problem, Department of Computing and Information Science, Ulniversity of Guelph, Ontario, preprint.Google Scholar
  16. [16]
    Christoff Hoffmann, Group Theoretic Algorithms and Graph Isomorphism, Lecture Notes in Computer Science #136, Springer-Verlag, New York, 1982.Google Scholar
  17. [17]
    Andrew Kirk, Efficiency considerations in the canonical labelling of graphs, Technical report TR-CS-85–05, Computer Science Department, Australian National University (1985).Google Scholar
  18. [18]
    William Kocay, Groups and Graphs, a Macintosh application for graph theory, J. Combinatorial Mathematics and Combinatorial Computing 3 (1988), 195–206.zbMATHGoogle Scholar
  19. [19]
    J.S. Leon, An algorithm for computing the automorphism group of a Hadamard matrix, J. Combinatorial Theory 27A (1979) 289–306.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Eugene M. Luks, Isomorphism of graphs of bounded valence can be tested in polynomial time, Proc. 21st IEEE Symp. on the Foundations of Comp. Sci., Rochester, N.Y., 1980, 42–49.Google Scholar
  21. [21]
    Rudi Mathon, Sample graphs for isomorphism testing, Conressus Numerantium 21 (1978) 499–517.Google Scholar
  22. [22]
    Brendan McKay, Topics in Computational Graph Theory, Ph.D. Thesis, University of Melbourne, 1980.Google Scholar
  23. [23]
    Brendan McKay, Nauty User’s Guide (Version 1.5), Computer Science Department, Australian National University.Google Scholar
  24. [24]
    Brendan McKay, Practical graph isomorphism, Conressus Numerantium 30 (1981), 45–87.Google Scholar
  25. [25]
    Brendan McKay, Backtrack Programming and the Graph Isomorphism Problem, M.Sc. Thesis, University of Melbourne, 1976.Google Scholar
  26. [26]
    R.C. Read and D.G. Corneil, The graph isomorphism disease, J. Graph Theory 1 (1977), 339–363.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    Mark Allen Weiss, Data Structures and Algorithm Analysis, Benjamin Cummings, Redwood City, California, 1992.Google Scholar
  28. [28]
    Helmut Wielandt, Finite Permutation Groups, Academic Press, New York, 1964.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • William Kocay
    • 1
  1. 1.Department of Computer ScienceUniversity of ManitobaWinnipegCanada

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