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**Natural bijections between directed and undirected self-complementary graphs.**
*(English)*
Zbl 0659.05051

In this paper the author gives a construction which establishes a bijection between the set of selfcomplementary directed graphs on 2k vertices and the set of selfcomplementary graphs on 4k vertices. (The fact that these two sets are equinumerous was proved by the reviewer many years ago.) A similar construction, also given, establishes the bijection between selfcomplementary directed graphs with loops on 2k vertices and selfcomplementary graphs on \(4k+1\) vertices.

The author has kindly pointed out to the reviewer a misprint on the next- to-last line of page 364, namely that the subscripts in the first expression on that line should be interchanged. The reviewer also notes some confusion between vertices of G and of H, which obscures the meaning of this vital paragraph.

The author has kindly pointed out to the reviewer a misprint on the next- to-last line of page 364, namely that the subscripts in the first expression on that line should be interchanged. The reviewer also notes some confusion between vertices of G and of H, which obscures the meaning of this vital paragraph.

Reviewer: R.C.Read

### MSC:

05C20 | Directed graphs (digraphs), tournaments |

05C30 | Enumeration in graph theory |

05C75 | Structural characterization of families of graphs |

### References:

[1] | BOSÁK J.: Rozklady grafov. (Decompositions of Graphs.) Veda, Bratislava 1986. |

[2] | MORRIS P.A.: On self-complementary graphs and digraphs. Proceedings of the fifth Southeastern conference on combinatorics, graph theory and computing (Florida Atlantic University, Boca Raton 1974). Hofìman F. et al., Congr. Num., Utilitas Math. Winnipeg 1974. · Zbl 0309.05127 |

[3] | READ R. C.: On the number of self-complementary graphs and digraphs. J. London Math. Soc. 38, 1963, 99-104. · Zbl 0116.15001 · doi:10.1112/jlms/s1-38.1.99 |

[4] | RINGEL G.: Selbstkomplementäre Graphen. Archiv der Math. 14, 1963, 354-358. · Zbl 0114.40102 · doi:10.1007/BF01234967 |

[5] | SACHS H.: Über selbstkomplementäre Graphen. Publ. Math. Debrecen 9, 1962, 270-288. · Zbl 0119.18904 |

[6] | WILLE D.: On the enumeration of self-complementary m-placed relations. Discrete Math. 10, 1974, 189-192. · Zbl 0289.05120 · doi:10.1016/0012-365X(74)90033-8 |

[7] | WILLE D.: Enumeration of self-complementary structures. J. Combin. Theory (B) 25, 1978, 143-150. · Zbl 0331.05005 · doi:10.1016/0095-8956(78)90034-5 |

[8] | ZELINKA B.: Decomposition of a digraph into isomorphic subgraphs. Časop. pěst. mat. 93, 1968, 92-100. · Zbl 0197.50504 |

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