Reversing the arcs of any 3-circuit of a tournament, the score vector is unchanged; therefore the class of regular tournaments is closed under this operation. Here we prove that the number of non-isomorphic, non-symmetric tournaments obtained by reversal from a particular regular tournament on n vertices is equal to n2-9/24 – 1 for n = 0 (mod 3) and n2-1/24 – 2 otherwise. Moreover, we generate all the non-isomorphic regular tournaments of order 9 and present their interchange graph.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics