63.6 JohnsonGraph

JohnsonGraph( n, e )

This function returns a graph gamma isomorphic to the Johnson graph, whose vertices are the e-subsets of {1,...,<n>}, with x joined to y if and only if |x cap y| = <e>-1. The group associated with gamma is image of the the symmetric group S_<n> acting on the e-subsets of {1,ldots,<n>}.

    gap> JohnsonGraph(5,3);
    rec(
      isGraph := true,
      order := 10,
      group := Group( ( 1, 8)( 2, 9)( 4,10), ( 1, 5)( 2, 6)( 7,10),
        ( 1, 3)( 4, 6)( 7, 9), ( 2, 3)( 4, 5)( 7, 8) ),
      schreierVector := [ -1, 4, 3, 4, 2, 3, 4, 1, 3, 2 ],
      adjacencies := [ [ 2, 3, 4, 5, 7, 8 ] ],
      representatives := [ 1 ],
      names := [ [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 2, 5 ], [ 1, 3, 4 ],
          [ 1, 3, 5 ], [ 1, 4, 5 ], [ 2, 3, 4 ], [ 2, 3, 5 ],
          [ 2, 4, 5 ], [ 3, 4, 5 ] ],
      isSimple := true ) 

Previous Up Top Next
Index