Abstract Using algorithms implicit in the classification of SL (2, Z) SL (2, Z) -orbits of primitive origamis in the stratum H (2) H (2) due to Hubert–Lelièvre and McMullen, we give diameter bounds on the resulting orbit graphs. Since the machinery of McMullen from H (2) H (2) is generalised and reused in Lanneau and Nguyen’s classification of the orbits of Prym eigenforms in H (4) H (4) and H (6) H (6), we are also able to obtain diameter bounds for the orbit graphs in this setting as well. In each stratum, we obtain diameter bounds of the form O (N^2/3 N) O (N 2 / 3 log N), where N is the size of the orbit graph.
Jeffreys et al. (Thu,) studied this question.