# -*- GAP -*-

Delta19i :=
rec(
  adjacencies := [ [ 5, 16 ], [ 5, 17 ], [ 5, 18 ], [ 5, 19 ], [ 1, 2, 3, 4 ], [ 10, 16 ], [ 10, 19 ], [ 10, 17 ], 
      [ 10, 18 ], [ 6, 7, 8, 9 ], [  ], [ 16, 18 ], [ 16, 19 ], [ 17, 18 ], [ 17, 19 ], [ 1, 6, 12, 13 ], 
      [ 2, 8, 14, 15 ], [ 3, 9, 12, 14 ], [ 4, 7, 13, 15 ] ],
  autGroup := Group( [ ( 3, 4)( 7, 9)(12,13)(14,15)(18,19), ( 2, 6)( 3,13)( 4,12)( 5,16)( 7,14)( 9,15)(10,17)(18,19), 
      ( 1, 2)( 6, 8)(12,14)(13,15)(16,17), ( 1, 3, 2, 4)( 6, 9, 8, 7)(12,14,15,13)(16,18,17,19) ] ),
  forms := [ rec(
          forms := [ [ "[-132] + U(2) + U(2)", "[-4] + [-4, -2, -12] + [4, 2, 4]", "[-4, -2, -12] + U(2) + [12]" ] ],
          h := 4 ), rec(
          forms := [ [  ] ],
          h := 8 ), rec(
          forms := [ [ "[-68] + U(2) + U(2)" ] ],
          h := 12 ), rec(
          forms := [ [ "[-36] + U(2) + U(2)" ], [ "[-4] + U(2) + U(2)" ] ],
          h := 16 ) ],
  group := Group( [ () ] ),
  h := [ 4, 8, 12, 16 ],
  info := rec(
      bipartite := true,
      distance_regular := false,
      girth := 6,
      pencils := [ [ 4, 6 ], [ 2, 12 ], [ 0, 1 ] ],
      regular := false,
      transitive := -1 ),
  isGraph := true,
  isSimple := true,
  names := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 ],
  order := 19,
  real := [ 4, 8, 12, 16 ],
  representatives := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 ],
  schreierVector := [ -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19 ] );

