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7 results

  • An easier enumeration of self-complementary graphs

  • C. R. J. Clapham
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 27 / Issue 2 / June 1984
    Published online by Cambridge University Press:
    20 January 2009, pp. 181-183
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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.