Geodesic
Polynomial-time recognizing and isomorphism testing for cyclic tournaments
Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part 5, Tome 192 (1991), pp. 74-111

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The purpose of the paper is to study isomorphism problem for cyclic tournaments (tournament is a complete directed graph and it is cyclic if its automorphism group containes a regular cyclic subgroup). The main result is a polynomial-time algorithm for constructing all non conjugated regular cyclic subgroups of odd order permutation group. Based on it a polynomial-time procedures for cyclic tournaments recognizing, constructing of its, canonical form and generators of automorphism group are presented. Used tools include the method of Schur rings. 
@article{ZNSL_1991_192_a4,
     author = {I. N. Ponomarenko},
     title = {Polynomial-time recognizing and isomorphism testing for cyclic tournaments},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {74--111},
     publisher = {mathdoc},
     volume = {192},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_192_a4/}
}
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I. N. Ponomarenko. Polynomial-time recognizing and isomorphism testing for cyclic tournaments. Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part 5, Tome 192 (1991), pp. 74-111. http://geodesic.mathdoc.fr/item/ZNSL_1991_192_a4/