63.50 PointGraph

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 

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