A054595 -id:A054595 - cp's OEIS frontend

A177451 Partial sums of A054595.

1, 4, 26, 281, 3602, 56550, 1121538, 26193063, 693887458, 20808594004, 699641607622, 26001947464541, 1059148042622186, 47015706166302146, 2260884753582320442, 117153802097975691651, 6513779162975806691634

Offset: 3

Jonathan Vos Post, May 09 2010

nonn

Partial sums of number of labeled 2-connected minimally 2-edge-connected graphs by nodes. The only prime in the partial sum values shown is 281.

			a(6) = 1 + 3 + 22 + 255 = 281 is prime.

Cf. A054595, A054317, A001072, A054596.

a(n) = SUM[i=3..n] A054595(i).

A003317 Number of unlabeled minimally 2-connected graphs with n nodes (also called "blocks").

Original entry on oeis.org

1, 1, 2, 3, 6, 12, 28, 68, 184, 526, 1602, 5075, 16711, 56428, 195003, 685649, 2447882, 8850157, 32359428, 119492766, 445236635, 1672636369, 6331624545, 24138404479, 92640942148, 357805122286, 1390318899884, 5433781135206

Offset: 3

N. J. A. Sloane

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

A. M. Hobbs, A catalog of minimal blocks, J. Res. National Bureau Standards, B 77 (1973), 53-60.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Audace A. V. Dossou-Olory, Cut and pendant vertices and the number of connected induced subgraphs of a graph, arXiv:1910.04552 [math.CO], 2019.
A. M. Hobbs, A catalog of minimal blocks, J. Res. National Bureau Standards, B 77 (1973), 53-60. (Annotated scanned copy)
Hu, Guan Zhang; Liu, Guo Qing; Liu, Shi; He, Jian Ping; Enumeration of minimally 2-connected graphs by means of group theory, (Chinese) Acta Math. Appl. Sinica 12 (1989), no. 2, 164-173.
S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Thesis, University of Georgia, 2000. [Local copy]
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000. [Local copy]

Cf. A054316, A054317, A002218.

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

A054317 Number of unlabeled 2-connected minimally 2-edge-connected graphs with n nodes.

Original entry on oeis.org

1, 1, 2, 3, 5, 10, 19, 42, 92, 225, 564, 1501, 4127, 11809, 34713, 104904, 323778, 1019538, 3265502, 10624881, 35065697, 117289911, 397290416, 1362060455, 4724272231, 16572501190, 58782486855, 210782826628, 763991002957

Offset: 3

Sridar K. Pootheri (sridar(AT)math.uga.edu), Feb 25 2000

References also contain the edge breakups for each term.

S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Thesis, University of Georgia, 2000. [Local copy]
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000. [Local copy]

Cf. A054316, A003317, A001072.

A054316 Number of unlabeled 2-connected 3-edge-connected graphs with n nodes.

Original entry on oeis.org

1, 3, 19, 149, 2578, 84127, 5201474, 577043450, 113371887160, 39618007594177, 24916462201698733, 28563626901315427552, 60366734333061918085970, 237406975833857522512566844, 1750330441805919888169149998870

Offset: 4

Sridar K. Pootheri (sridar(AT)math.uga.edu), Feb 25 2000

S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Thesis, University of Georgia, 2000. [Local copy]
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000. [Local copy]

Cf. A054317, A003317.

A054596 Number of labeled minimally 2-edge-connected graphs by nodes.

Original entry on oeis.org

1, 3, 37, 435, 6996, 134428, 3094785, 82061325, 2473950880, 83606473566, 3132506471139, 128918727009163, 5784184164416490, 281105943314654760, 14716271275161095761, 825944690635111256697, 49490362937885427672552

Offset: 3

Sridar K. Pootheri (sridar(AT)math.uga.edu), Apr 14 2000

The reference given here also contains the edge breakups for each node given here.

S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Thesis, University of Georgia, 2000. [Local copy]
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000. [Local copy]

Cf. A054317, A001072, A054595.

A054853 Number of labeled 3-edge-connected graphs by nodes.

Original entry on oeis.org

1, 26, 1858, 236926, 53456032, 21493860332, 15580415345706, 20666613177952152, 50987341499153087708, 237747594646361178843768, 2125708461695379843278043006, 36886187376770375742178892122216

Offset: 4

Sridar K. Pootheri (sridar(AT)math.uga.edu), Apr 14 2000

The reference given here also contains the edge breakups for each node given here.

S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Thesis, University of Georgia, 2000. [Local copy]
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000. [Local copy]

Cf. A054316, A038207, A257947.

A054597 Number of labeled 2-connected 3-edge-connected graphs by nodes.

Original entry on oeis.org

1, 26, 1858, 236856, 53448752, 21492710960, 15580155490586, 20666523608722248, 50987290998908713436, 237747545131143536698656, 2125708373867783657045636502, 36886187089139407854559886683336

Offset: 4

Sridar K. Pootheri (sridar(AT)math.uga.edu), Apr 14 2000

The reference given here also contains the edge breakups for each node given here.

S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Thesis, University of Georgia, 2000. [Local copy]
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000. [Local copy]

Cf. A054316, A054853.

Cf. A005643.

A054594 Number of labeled minimally 2-connected graphs by nodes.

Original entry on oeis.org

1, 3, 22, 255, 3951, 76468, 1773108, 48018645, 1488656845, 51989095026, 2019934308294, 86440374376447, 4040615973961035, 204882667497974040, 11202622636253431336, 657174516317371860777, 41178215707421481322713

Offset: 3

Sridar K. Pootheri (sridar(AT)math.uga.edu), Apr 14 2000

S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Counting classes of labeled 2-connected graphs, M.S. Thesis, University of Georgia, 2000. [Local copy]
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000.
S. K. Pootheri, Characterizing and counting classes of unlabeled 2-connected graphs, Ph. D. Dissertation, University of Georgia, 2000. [Local copy]

Cf. A003317.

cp's OEIS Frontend

A177451 Partial sums of A054595.

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A003317 Number of unlabeled minimally 2-connected graphs with n nodes (also called "blocks").

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A054317 Number of unlabeled 2-connected minimally 2-edge-connected graphs with n nodes.

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A054316 Number of unlabeled 2-connected 3-edge-connected graphs with n nodes.

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A054596 Number of labeled minimally 2-edge-connected graphs by nodes.

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A054853 Number of labeled 3-edge-connected graphs by nodes.

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A054597 Number of labeled 2-connected 3-edge-connected graphs by nodes.

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A054594 Number of labeled minimally 2-connected graphs by nodes.

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