63.51 EdgeGraph

EdgeGraph( gamma )

This function returns the edge graph, also called the line graph, of the simple graph gamma.

This edge graph delta has the unordered edges of gamma as vertices, and e is joined to f in delta precisely when |e cap f|=1.

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

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