A348222 Number of uniquely-3-colorable graphs on n vertices.

1, 1, 3, 12, 72, 856, 17018, 531568

Offset: 3

Author

Gordon Royle, Oct 08 2021

Keywords

• nonn
• more

Comments

A graph is uniquely 3-colorable if there is a unique partition of its vertex set into 3 independent sets. This implies that every proper 3-coloring of the graph has this partition as its set of color classes.

Examples

			a(3) = 1 and  a(4) = 1 because the complete graph K3 and K4-e are the only such graphs on 3 and 4 vertices, respectively.
		

Crossrefs

Cf. A369227

Formula

a(n) = A369227(n,3). - Eric W. Weisstein, Jan 16 2024