A369223 Number of uniquely colorable simple graphs on n nodes.

1, 1, 2, 3, 6, 11, 35, 134, 1183, 21319, 761871

Offset: 0

Author

Eric W. Weisstein, Jan 16 2024

Keywords

• nonn
• more

Comments

The only disconnected uniquely colorable graphs are the empty graphs on n > 1 nodes.

Examples

			n = 1: singleton graph K_1 (1 graph).
n = 2: 2-empty graph, path graph P_2 (2 graphs).
n = 3: 3-empty graph, path graph P_3, triangle graph C_3 = K_3 (3 graphs).
n = 4: 4-empty graph, claw graph K_{1,3}, diamond graph K_{1,1,2} = K_4-e, P_4, square graph C_4, tetrahedral graph K_4 (6 graphs).
		

Links

• Eric Weisstein's World of Mathematics, Simple Graph.
• Eric Weisstein's World of Mathematics, Uniquely Colorable Graph.

Crossrefs

Cf. A001349.

Cf. A369227 (triangle by chromatic number).

Formula

a(n) = Sum_{k=1..n} A369227(n,k).