A222625 Number of simple connected well-covered graphs on n nodes.

1, 1, 1, 3, 6, 27, 108, 788, 9035, 196928, 7797877, 533938066

Offset

1,4

Comments

A graph is well-covered if its maximal independent vertex sets are of equal size.

Links

Table of n, a(n) for n=1..12.

Jonathan Baker, K. N. V. Meulen, A. Van Tuyl, Shedding vertices of vertex decomposable graphs, arXiv preprint arXiv:1606.04447 [math.CO], 2016.

F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version a1db88e

Eric Weisstein's World of Mathematics, Connected Graph

Eric Weisstein's World of Mathematics, Well-Covered Graph

Formula

a(n) = A222626(n) - A287025(n).

Inverse Euler transform of A222626. - Andrew Howroyd, Nov 03 2017

Mathematica

A222626 = {1, 2, 3, 7, 14, 46, 164, 996, 10195, 208168, 8016530, 542165050};
mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];
EULERi[b_] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i b[[i]] - Sum[c[[d]] b[[i - d]], {d, 1, i - 1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*Sum[mob[i, d] c[[d]], {d, 1, i}]]]; Return[a]];
EULERi[A222626] (* Jean-François Alcover, Feb 22 2019, after Andrew Howroyd *)

Crossrefs

Cf. A222626 (number of simple not-necessarily connected well-covered graphs).

Cf. A287025 (number of simple disconnected well-covered graphs).

Sequence in context: A215399 A215400 A215394 * A060170 A223143 A372039

Adjacent sequences: A222622 A222623 A222624 * A222626 A222627 A222628

Keyword

nonn,more

Author

Eric W. Weisstein, Feb 26 2013

Extensions

a(10) from Eric W. Weisstein, Aug 29 2013

a(11)-a(12) added using tinygraph by Falk Hüffner, Aug 15 2017

Status

approved