The use of Subsets is illustrated in the construction of the Petersen
graph as the third Odd Graph. The nth Odd Graph has its vertices
in correspondence with the (n - 1)-element subsets of
{ 1 ... 2n - 1 }, and an edge between two vertices if
and only if their corresponding sets have empty intersection.
> V := Subsets( {1 .. 2*n-1}, n-1) where n is 3;
> V;
{
{ 1, 5 },
{ 2, 5 },
{ 1, 3 },
{ 1, 4 },
{ 2, 4 },
{ 3, 5 },
{ 2, 3 },
{ 1, 2 },
{ 3, 4 },
{ 4, 5 }
}
> E := { {u, v} : u,v in V | IsDisjoint(u, v) };
> Petersen := Graph< V | E >;