A circuit in which an entire graph is traversed in one route. Examples of curves that can be traced unicursally are
the Mohammed sign and unicursal hexagram.

The numbers of distinct unicursal polygrams that can be formed from points on circle with no two adjacent for , 2, ... are 1, 0, 0, 0, 1, 3, 23, 177, 1553, ... (OEIS A002816). For , these are given by the sum

This sequence is also given by the recurrence equation