Brockman–Kay–Snively's gucycle conjecture for unlabeled graphs

Let a gucycle be a cyclic ordering whose windows represent each isomorphism class of graphs on $n$ vertices exactly once. Brockman–Kay–Snively's conjecture. For each $n\neq 2$, there exists a gucycle of isomorphism classes of graphs on $n$ vertices. The conjecture was stated by Brockman, Kay, and Snively, who found a gucycle for $n=4$; it is false for $n=3$, where a guword rather than a gucycle is possible.