Geodesic
Self-Converse Tournaments
Canadian mathematical bulletin, Tome 22 (1979) no. 1, pp. 23-27

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Let T n denote a tournament with vertices labelled 1, ..., n. Any undefined terms can be found in [5]. The converse of T n is the tournament obtained by reversing the orientation of all the arcs in T n. A tournament is called self-converse (s.c.) if . The transitive tournaments are examples of s.c. tournaments. In this paper we provide a structural characterization of s.c. tournaments and we also characterize the score vectors of s.c. tournaments. 
Eplett, W. J. R. Self-Converse Tournaments. Canadian mathematical bulletin, Tome 22 (1979) no. 1, pp. 23-27. doi: 10.4153/CMB-1979-004-6
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     doi = {10.4153/CMB-1979-004-6},
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