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 n points on circle with no two adjacent for n = 1, 2, ... are 1, 0, 0, 0, 1, 3, 23, 177, 1553, ... (OEIS A002816). For n>2, these are given by the sum a(n) = (-1)^n + 1/2(n - 1)! + sum_(k = 1)^(n - 1) sum_(j = 1)^k ((-1)^k 2^(j - 1)(k - 1 j - 1)(n - k j) n(n - k - 1)!)/(n - k).

Eulerian cycle | graph cycle | hexagram | Königsberg bridge problem | Mohammed sign | traceable graph