EdgeOrbitsGraph( G, E )
EdgeOrbitsGraph( G, E, n )
This is a common way of constructing a graph in GRAPE.
This function returns the (directed) graph with vertex set {1,...,<n>}, edge set cup _{e in <E>}, e^<G>, and associated (permutation) group G, which must act naturally on {1,...,<n>}. The parameter E should be a list of edges (lists of length 2 of vertices), although a singleton edge will be understood as an edge list of length 1. The parameter n may be omitted, in which case the number of vertices is the largest point moved by a generator of G.
Note that G may be the trivial permutation group (Group( () )
in
GAP notation), in which case the (directed) edges of gamma are
simply those in the list E.
gap> EdgeOrbitsGraph( Group((1,3),(1,2)(3,4)), [[1,2],[4,5]], 5 ); rec( isGraph := true, order := 5, group := Group( (1,3), (1,2)(3,4) ), schreierVector := [ -1, 2, 1, 2, -2 ], adjacencies := [ [ 2, 4, 5 ], [ ] ], representatives := [ 1, 5 ], isSimple := false )
GAP 3.4.4