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Number of connected chordal graphs on n vertices.
16

%I #42 Feb 16 2025 08:32:39

%S 1,1,2,5,15,58,272,1614,11911,109539,1247691,17566431,305310547,

%T 6558690953,174688164414

%N Number of connected chordal graphs on n vertices.

%H F. Hüffner, <a href="https://github.com/falk-hueffner/tinygraph">tinygraph</a>, software for generating integer sequences based on graph properties, version 6e0a59d

%H Tim Kemp, <a href="http://essay.utwente.nl/82685/1/Kemp-MA-EEMCS.pdf">An algorithmic approach to a conjecture of Chvátal on toughness and hamiltonicity of graphs</a>, M. Sc. Thesis, University of Twente (Netherlands, 2020).

%H B. D. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/data/graphs.html">Chordal graphs</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChordalGraph.html">Chordal Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>

%F a(n) = A048193(n) - A287427(n). - _Eric W. Weisstein_, May 25 2017

%F Inverse Euler transform of A048193. - _Andrew Howroyd_, Nov 03 2017

%Y Cf. A048193 (not-necessarily connected chordal graphs).

%Y Cf. A287427 (disconnected chordal graphs).

%Y Cf. A048194.

%K nonn,nice,more,changed

%O 1,3

%A _Gordon F. Royle_

%E a(12) added by _Gordon F. Royle_, Aug 05 2008

%E a(13) and a(14) added using tinygraph by _Falk Hüffner_, Jan 15 2016

%E a(15) added by _Brendan McKay_, Jan 07 2019