# 63.54 BipartiteDouble

`BipartiteDouble( gamma )`

This function returns the bipartite double of the graph gamma, as defined in BCN89.

```    gap> gamma := JohnsonGraph(4,2);
rec(
isGraph := true,
order := 6,
group := Group( (1,5)(2,6), (1,3)(4,6), (2,3)(4,5) ),
schreierVector := [ -1, 3, 2, 3, 1, 2 ],
adjacencies := [ [ 2, 3, 4, 5 ] ],
representatives := [ 1 ],
names := [ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 2, 3 ], [ 2, 4 ],
[ 3, 4 ] ],
isSimple := true )
gap> IsBipartite(gamma);
false
gap> delta := BipartiteDouble(gamma);
rec(
isGraph := true,
order := 12,
group := Group( ( 1, 5)( 2, 6)( 7,11)( 8,12), ( 1, 3)( 4, 6)( 7, 9)
(10,12), ( 2, 3)( 4, 5)( 8, 9)(10,11), ( 1, 7)( 2, 8)( 3, 9)
( 4,10)( 5,11)( 6,12) ),
schreierVector := [ -1, 3, 2, 3, 1, 2, 4, 4, 4, 4, 4, 4 ],
adjacencies := [ [ 8, 9, 10, 11 ] ],
representatives := [ 1 ],
isSimple := true,
names := [ [ [ 1, 2 ], "+" ], [ [ 1, 3 ], "+" ], [ [ 1, 4 ], "+" ],
[ [ 2, 3 ], "+" ], [ [ 2, 4 ], "+" ], [ [ 3, 4 ], "+" ],
[ [ 1, 2 ], "-" ], [ [ 1, 3 ], "-" ], [ [ 1, 4 ], "-" ],
[ [ 2, 3 ], "-" ], [ [ 2, 4 ], "-" ], [ [ 3, 4 ], "-" ] ] )
gap> IsBipartite(delta);
true ```

GAP 3.4.4
April 1997