63.56 CollapsedIndependentOrbitsGraph

CollapsedIndependentOrbitsGraph( G, gamma )
CollapsedIndependentOrbitsGraph( G, gamma, N )

Given a subgroup G of the automorphism group of the graph gamma, this function returns a graph isomorphic to delta, defined as follows. The vertices of delta are those G-orbits of the vertices of gamma that are independent sets, and x is not joined to y in delta if and only if x cup y is an independent set in gamma.

If the optional parameter N is given, then it is assumed to be a subgroup of Aut(<gamma>) preserving the set of G-orbits of the vertices of gamma (for example, the normalizer in gamma.group of G). This information can make the function more efficient.

    gap> G := Group( (1,2) );;
    gap> gamma := NullGraph( SymmetricGroup(3) );;
    gap> CollapsedIndependentOrbitsGraph( G, gamma );
    rec(
      isGraph := true,
      order := 2,
      group := Group( () ),
      schreierVector := [ -1, -2 ],
      adjacencies := [ [  ], [  ] ],
      representatives := [ 1, 2 ],
      isSimple := true,
      names := [ [ 1, 2 ], [ 3 ] ] ) 

Previous Up Top Next
Index