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Graphs and Combinatorics

, Volume 30, Issue 2, pp 471–477 | Cite as

Enumeration of Bipartite Self-Complementary Graphs

  • Makoto Ueno
  • Shinsei Tazawa
Original Paper

Abstract

Let e(m, n), o(m, n), bsc(m, n) be the number of unlabelled bipartite graphs with an even number of edges whose partite sets have m vertices and n vertices, the number of those with an odd number of edges, and the number of unlabelled bipartite self-complementary graphs whose partite sets have m vertices and n vertices, respectively. Then this paper shows that the equality bsc(m, n) = e(m, n) − o(m, n) holds.

Keywords

Bipartite self-complementary graph Burnside’s Lemma Automorphism group 

Mathematics Subject Classification (2000)

05A15 05C25 05C30 

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Copyright information

© Springer Japan 2012

Authors and Affiliations

  1. 1.NSC CO.,LTD.ToyonakaJapan
  2. 2.Faculty of Applied SociologyKinki UniversityHigashi-OsakaJapan

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