Corrected 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. Corrected gucycle conjecture. For each $n\geq 4$, there exists a gucycle of isomorphism classes of graphs on $n$ vertices. This corrects the Brockman–Kay–Snively conjecture, which fails for $n=3$; the general existence question remains unresolved in the source.