63.57 CollapsedCompleteOrbitsGraph

CollapsedCompleteOrbitsGraph( G, gamma )
CollapsedCompleteOrbitsGraph( G, gamma, N )

Given a subgroup G of the automorphism group of the simple 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 on which complete subgraphs are induced in gamma, and x is joined to y in delta if and only if xnot=y and the subgraph of gamma induced on x cup y is a complete graph.

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

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