Dual tournament

Dual tournament --- двойственный турнир.

Let [math]\displaystyle{ T = (V,A) }[/math] be a finite tournament with [math]\displaystyle{ n }[/math] vertices. The dual of [math]\displaystyle{ T }[/math] is the tournament [math]\displaystyle{ T^{\ast} = (V,A^{\ast}) }[/math], defined by: for all [math]\displaystyle{ x,y \in V }[/math], [math]\displaystyle{ (y,x) \in A^{\ast} }[/math] if and only if [math]\displaystyle{ (x,y) \in A }[/math].

The tournament [math]\displaystyle{ T }[/math] is selfdual, when [math]\displaystyle{ T }[/math] is isomorphic to [math]\displaystyle{ T^{\ast} }[/math].