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An easier enumeration of self-complementary graphs

Published online by Cambridge University Press:  20 January 2009

C. R. J. Clapham
C. R. J. Clapham
Affiliation:
University of Aberdeen
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The number of self-complementary (s.c.) graphs and digraphs with a given number of vertices was found by R. C. Read in [1]. That paper used a special case of De Bruijn's generalisation of Polya's theorem that involved the cycle-index of Gn, the group of permutations of pairs of vertices induced by permutations of the vertices. We obtain Read's formulae by using only well-known elementary facts about s.c. graphs and their complementing permutations.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 2 , June 1984 , pp. 181 - 183
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Read, R. C., On the number of self-complementary graphs and digraphs, J. London Math. Soc. 38 (1963), 99–104.CrossRefGoogle Scholar
2.Berge, C., Principles of Combinatorics (Academic Press, New York and London, 1971).Google Scholar