Polynomial-time recognizing and isomorphism testing for cyclic tournaments

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.