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Computing automorphisms and canonical labellings of graphs

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 686))

Abstract

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.

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References

  1. M. Behzad and G. Chartrand, Introduction to the theory of graphs, Allyn and Bacon, Boston (1971).

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  2. D.G. Corneil, Graph Isomorphism, Ph.D. Thesis, Univ. of Toronto (1968).

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  3. B.D. McKay, Backtrack programming and the graph isomorphism problem, M.Sc. Thesis, Univ. of Melbourne (1976).

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  4. B.D. McKay, "Backtrack programming and isomorph rejection on ordered subsets", to appear in Proc. 5th Australian Conf. on Combin. Math. (1976).

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  5. R. Parris, The coding problem for graphs, M.Sc. Thesis, Univ. of West Indies (1968).

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  6. J.P. Steen, "Principle d'un algorithme de recherche d'un isomorphisme entre deux graphes", RIRO, R-3, 3 (1969), 51–69.

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  7. H. Wielandt, Finite permutation groups, Academic Press, New York and London (1964).

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D. A. Holton Jennifer Seberry

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© 1978 Springer-Verlag

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McKay, B.D. (1978). Computing automorphisms and canonical labellings of graphs. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062536

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  • DOI: https://doi.org/10.1007/BFb0062536

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08953-7

  • Online ISBN: 978-3-540-35702-5

  • eBook Packages: Springer Book Archive

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