Graphs related to principal autotopisms of Latin squares

Abstract

Latin squares of order nare equivalent to 1-factorizations of Kn,n. In this way, fixed a principal isotopism Θ=(α,β,ε)∈S3n, where Sn is the symmetric group of the set N={0,1, ..., n−1}, we are going to study in this paper the set of graphs related to Θ when this last one is a principal autotopism of a Latin square. To do it, the number ∆R(Θ) of reduced Latin squares having Θ as a principal autotopism is studied.