PointGraph( gamma )
PointGraph( gamma, v )
Assuming that gamma is simple, connected, and bipartite, this function
returns the induced subgraph on the connected component of
DistanceGraph(gamma,2)
containing the vertex v (default:
<v>=1).
Thus, if gamma is the incidence graph of a connected geometry, and v represents a point, then the point graph of the geometry is returned.
gap> BipartiteDouble( CompleteGraph(SymmetricGroup(4)) );; gap> PointGraph(last); rec( isGraph := true, order := 4, group := Group( (3,4), (2,4), (1,4) ), schreierVector := [ -1, 2, 1, 3 ], adjacencies := [ [ 2, 3, 4 ] ], representatives := [ 1 ], isSimple := true, names := [ [ 1, "+" ], [ 2, "+" ], [ 3, "+" ], [ 4, "+" ] ] ) gap> IsCompleteGraph(last); true
GAP 3.4.4