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A000080 Number of nonisomorphic minimal triangle graphs.
(Formerly M1173 N0450)
1, 1, 2, 4, 9, 19, 48, 117, 307, 821, 2277, 6437, 18634, 54775, 163703, 495529, 1518706, 4703848, 14714754, 46444979, 147832051, 474229588, 1532565644 (list; graph; refs; listen; history; text; internal format)



Let T be a set of triples (sets of three distinct points) from a set of n points. The graph G(T) has a vertex for each point, with two vertices joined by an edge if the two points belong to one of the triples. Then a(n) is the number of ways to choose T so that G(T) is connected and minimal, meaning that it becomes disconnected if any triple is omitted. - N. J. A. Sloane, Jan 22 2014


N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=3..25.

R. Bowen, The generation of minimal triangle graphs, Math. Comp. 21 (1967), 248-250.

Martin Fuller, C program

N. J. A. Sloane, Illustration of initial terms (annotated version of figure from Bowen 1967).


The triples on n = 3 through 6 points are (see "Illustration" link): 3 : ABC; 4 : ABC, ABD; 5 : ABC, ADE; and ABC, ABD, ABE, 6 : ABD, BCD, DEF; ABC, BCD, DEF; ABF, BCD, DEF; ABC, ABD, ABE, ABF. - N. J. A. Sloane, Jan 22 2014


Cf. A048781.

Sequence in context: A052328 A133228 A036717 * A153447 A076893 A176501

Adjacent sequences:  A000077 A000078 A000079 * A000081 A000082 A000083




N. J. A. Sloane


Three more terms from Arlin Anderson (starship1(AT)gmail.com)

a(17)-a(25) from Martin Fuller, Mar 23 2015



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Last modified December 12 21:50 EST 2017. Contains 295954 sequences.