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Number of chordal graphs (or triangulated graphs) on n vertices.
5

%I #28 Feb 16 2025 08:32:39

%S 1,2,4,10,27,94,393,2119,14524,126758,1392387,19109099,326005775,

%T 6905776799,181945055235

%N Number of chordal graphs (or triangulated graphs) on n vertices.

%C Graphs having no induced cycles of any length > 3, so every cycle in the graph has a chord, or is "triangulated".

%C All such graphs are perfect.

%C Euler transform of A048192. - _Eric M. Schmidt_, Mar 25 2015

%C Conjectured partial sums of A079456. - _Sean A. Irvine_, Jun 25 2022

%H S. Hougardy, <a href="http://www.or.uni-bonn.de/~hougardy/">Home Page</a>

%H S. Hougardy, <a href="http://dx.doi.org/10.1016/j.disc.2006.05.021">Classes of perfect graphs</a>, Discr. Math. 306 (2006), 2529-2571.

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

%F a(n) = A048192(n) + A287427(n).

%Y Cf. A048192 (connected chordal graphs).

%Y Cf. A287427 (disconnected chordal graphs).

%Y Cf. A048194.

%K nonn,more,changed

%O 1,2

%A _Gordon F. Royle_

%E Edited by _N. J. A. Sloane_, Jul 04 2008

%E a(12) added (using A048192) by _Eric M. Schmidt_, Mar 25 2015

%E a(13) and a(14) added (using A048192) by _Falk Hüffner_, Jan 15 2016

%E a(15) added (using A048192) by _Jakub Jablonski_, Sep 15 2020