chess - Is the space of solutions to the Queens Domination Problem connected?

Revised and correct:

589 equivalence classes.

http://www.math.ucsd.edu/~etressle/classes.txt

It seems that the pairs (#vertices,#components) are (1,388) (2,100) (3,40) (4,34) (5,20) (18,4) (20,2) (3804,1) – damiano 15 hours ago

1: Class I.D. 2, 4, 5, 6, 7,..., 589.
2: Class I.D. 22, 29, 35, 47, 48,..., 579.
3: Class I.D. 28, 33, 38, 49, 58,..., 574.
4: Class I.D. 13, 90, 95, 126, 141,..., 576. 
5: Class I.D. 32, 37, 62, 89, 97,..., 395. 
18: Class I.D. 17, 31, 185, 303.
20: Class I.D. 3, 75.
3804: Class I.D. 1.