CIRCULANT GRAPHS with N <= 20 vertices: is G*(X) = G(X)?
   N  sets     C     Q     ?
   2     2     2     0     0
   3     2     2     0     0
   4     4     2     2     0
   5     4     3     1     0
   6     8     5     3     0
   7     8     7     1     0
   8    16    10     6     0
   9    16    14     2     0
  10    32    22    10     0
  11    32    31     1     0
  12    64    45    19     0
  13    64    63     1     0
  14   128   106    22     0
  15   128   118    10     0
  16   256   218    38     0
  17   256   255     1     0
  18   512   457    55     0
  19   512   511     1     0
  20  1024   934    90     0
  undecided graphs: none
THEOREM 7.5, graphs with p^2 vertices having quantum symmetry (S meets the units in a union of cosets of pZ):
  N=4 S=[]                     units in S: False  ('Q', 'empty')
  N=4 S=[1, 3]                 units in S: True   ('C', 'join')
  N=4 S=[2]                    units in S: False  ('Q', 'pair')
  N=4 S=[1, 2, 3]              units in S: True   ('C', 'complete')
  N=9 S=[]                     units in S: False  ('Q', 'empty')
  N=9 S=[3, 6]                 units in S: False  ('Q', 'pair')
  N=9 S=[1, 2, 4, 5, 7, 8]     units in S: True   ('C', 'join')
  N=9 S=[1, 2, 3, 4, 5, 6, 7, 8] units in S: True   ('C', 'complete')
THEOREM 7.2, dihedral type on Z_4 x Z_2^m: all the relations commutative for G*(X)?
  A = Z_4: graphs of dihedral type 2 (all), with G* = G proved 1, exceptions [[2]]
  A = Z_4x2: graphs of dihedral type 0 (all), with G* = G proved 0, exceptions []
  A = Z_4x2x2: graphs of dihedral type 0 (all), with G* = G proved 0, exceptions []
  A = Z_4x2x2x2: graphs of dihedral type 40 (sampled), with G* = G proved 40, exceptions []