A382212 Number of labeled Eulerian oriented graphs with n nodes without isolated vertices.

0, 0, 2, 6, 168, 6700, 726360, 202827786

Offset: 1

Author

Bert Dobbelaere, Mar 18 2025

Keywords

• nonn
• more

Comments

This sequence is similar to A007081 but imposes the restriction that the graphs contain no isolated vertices.

Each graph can be considered to represent a generalized rock-paper-scissors game for which a uniformly random strategy is optimal and no draw can be forced.

Examples

			For n=3, the only solutions are given by the directed cycles (1,2,3) and (1,3,2). Similarly, also n=4 only has directed cycles as solutions.
An example of a solution for n=5 is
  1 -> {5}
  2 -> {5}
  3 -> {4}
  4 -> {1,2}
  5 -> {3,4}
Disconnected solutions exist only for n >= 6.
		

Links

• Wikipedia, Rock paper scissors

Crossrefs

Cf. A007081.