|
%I #24 Feb 02 2024 09:05:41
%S 1,1,2,3,6,11,35,134,1183,21319,761871
%N Number of uniquely colorable simple graphs on n nodes.
%C The only disconnected uniquely colorable graphs are the empty graphs on n > 1 nodes.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SimpleGraph.html">Simple Graph</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UniquelyColorableGraph.html">Uniquely Colorable Graph</a>.
%F a(n) = Sum_{k=1..n} A369227(n,k).
%e n = 1: singleton graph K_1 (1 graph).
%e n = 2: 2-empty graph, path graph P_2 (2 graphs).
%e n = 3: 3-empty graph, path graph P_3, triangle graph C_3 = K_3 (3 graphs).
%e 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).
%Y Cf. A001349.
%Y Cf. A369227 (triangle by chromatic number).
%K nonn,more
%O 0,3
%A _Eric W. Weisstein_, Jan 16 2024
| 