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Number of unlabeled minimally 2-connected graphs with n nodes (also called "blocks").
(Formerly M0799)
10

%I M0799 #29 Jan 31 2022 01:23:38

%S 1,1,2,3,6,12,28,68,184,526,1602,5075,16711,56428,195003,685649,

%T 2447882,8850157,32359428,119492766,445236635,1672636369,6331624545,

%U 24138404479,92640942148,357805122286,1390318899884,5433781135206

%N Number of unlabeled minimally 2-connected graphs with n nodes (also called "blocks").

%C The Pootheri references also contain the edge breakups for each term.

%D A. M. Hobbs, A catalog of minimal blocks, J. Res. National Bureau Standards, B 77 (1973), 53-60.

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

%H Audace A. V. Dossou-Olory, <a href="https://arxiv.org/abs/1910.04552">Cut and pendant vertices and the number of connected induced subgraphs of a graph</a>, arXiv:1910.04552 [math.CO], 2019.

%H A. M. Hobbs, <a href="/A003317/a003317.pdf">A catalog of minimal blocks</a>, J. Res. National Bureau Standards, B 77 (1973), 53-60. (Annotated scanned copy)

%H Hu, Guan Zhang; Liu, Guo Qing; Liu, Shi; He, Jian Ping; <a href="http://en.cnki.com.cn/Article_en/CJFDTOTAL-YYSU198902004.htm">Enumeration of minimally 2-connected graphs by means of group theory</a>, (Chinese) Acta Math. Appl. Sinica 12 (1989), no. 2, 164-173.

%H S. K. Pootheri, <a href="https://athenaeum.libs.uga.edu/handle/10724/20082">Counting classes of labeled 2-connected graphs</a>, M.S. Dissertation, University of Georgia, 2000.

%H S. K. Pootheri, <a href="/A054595/a054595.pdf">Counting classes of labeled 2-connected graphs</a>, M.S. Thesis, University of Georgia, 2000. [Local copy]

%H S. K. Pootheri, <a href="https://athenaeum.libs.uga.edu/handle/10724/20083">Characterizing and counting classes of unlabeled 2-connected graphs</a>, Ph. D. Dissertation, University of Georgia, 2000.

%H S. K. Pootheri, <a href="/A003317/a003317_1.pdf">Characterizing and counting classes of unlabeled 2-connected graphs</a>, Ph. D. Dissertation, University of Georgia, 2000. [Local copy]

%Y Cf. A054316, A054317, A002218.

%K nonn,nice

%O 3,3

%A _N. J. A. Sloane_

%E More terms from Sridar K. Pootheri (sridar(AT)math.uga.edu), Feb 25 2000