A287427 -id:A287427 - cp's OEIS frontend

A048192 Number of connected chordal graphs on n vertices.

1, 1, 2, 5, 15, 58, 272, 1614, 11911, 109539, 1247691, 17566431, 305310547, 6558690953, 174688164414

Offset: 1

F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 6e0a59d
Tim Kemp, An algorithmic approach to a conjecture of Chvátal on toughness and hamiltonicity of graphs, M. Sc. Thesis, University of Twente (Netherlands, 2020).
B. D. McKay, Chordal graphs
Eric Weisstein's World of Mathematics, Chordal Graph
Eric Weisstein's World of Mathematics, Connected Graph

Cf. A048193 (not-necessarily connected chordal graphs).
Cf. A287427 (disconnected chordal graphs).
Cf. A048194.

a(n) = A048193(n) - A287427(n). - Eric W. Weisstein, May 25 2017

Inverse Euler transform of A048193. - Andrew Howroyd, Nov 03 2017

a(12) added by Gordon F. Royle, Aug 05 2008
a(13) and a(14) added using tinygraph by Falk Hüffner, Jan 15 2016
a(15) added by Brendan McKay, Jan 07 2019

A048193 Number of chordal graphs (or triangulated graphs) on n vertices.

Original entry on oeis.org

1, 2, 4, 10, 27, 94, 393, 2119, 14524, 126758, 1392387, 19109099, 326005775, 6905776799, 181945055235

Offset: 1

Gordon F. Royle

Graphs having no induced cycles of any length > 3, so every cycle in the graph has a chord, or is "triangulated".
All such graphs are perfect.
Euler transform of A048192. - Eric M. Schmidt, Mar 25 2015
Conjectured partial sums of A079456. - Sean A. Irvine, Jun 25 2022

S. Hougardy, Home Page
S. Hougardy, Classes of perfect graphs, Discr. Math. 306 (2006), 2529-2571.
Eric Weisstein's World of Mathematics, Chordal Graph

Cf. A048192 (connected chordal graphs).
Cf. A287427 (disconnected chordal graphs).
Cf. A048194.

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

Edited by N. J. A. Sloane, Jul 04 2008
a(12) added (using A048192) by Eric M. Schmidt, Mar 25 2015
a(13) and a(14) added (using A048192) by Falk Hüffner, Jan 15 2016
a(15) added (using A048192) by Jakub Jablonski, Sep 15 2020

cp's OEIS Frontend

A048192 Number of connected chordal graphs on n vertices.

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