Abstract Ovals of Order \(9\)

Massimo Giulietti1, Elisa Montanucci1
1DIPARTIMENTO DI MATEMATICA E INFORMATICA, UNIVERSITA DEGLI STUDI DI PERUGIA, VIA VANVITELLI, 1, 06123 PERUGIA, ITALY

Abstract

In this paper, it is shown that there are exactly \(5\) non-isomorphic abstract ovals of order \(9\), all of them projective. The result has been obtained via an exhaustive search, based on the classification of the \(1\)-factorizations of the complete graph with \(10\) vertices.