A003317 -id:A003317 - cp's OEIS frontend

A054595 Number of labeled 2-connected minimally 2-edge-connected graphs by nodes.

1, 3, 22, 255, 3321, 52948, 1064988, 25071525, 667694395, 20114706546, 678833013618, 25302305856919, 1033146095157645, 45956558123679960, 2213869047416018296, 114892917344393371209, 6396625360877830999983

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, A054596.

A324418 Number of minimally 4-connected non-isomorphic n-vertex graphs.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 5, 13, 83, 704, 8738, 136391

Offset: 1

Jens M. Schmidt, Mar 03 2019

Jens M. Schmidt, Data files in graph6 format

Cf. A003317, A324424.

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.

A366756 Number of minimally 1-tough unlabeled graphs on n nodes.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 2, 5

Offset: 1

Pontus von Brömssen, Oct 20 2023

A graph is minimally 1-tough if it is 1-tough but the removal of any of its edges makes it non-1-tough.

			For n >= 3, the cycle graph is minimally 1-tough. For 3 <= n <= 6, this is the only minimally 1-tough graph, so a(n) = 1.
For n = 7 and n = 8, the graphs with House of Graphs id's 536 and 36063, respectively, are also minimally 1-tough, and a(7) = a(8) = 2.
For n = 9, the a(9) = 5 minimally 1-tough graphs are (in graph6 format) "H?CidB?" (9-cycle), "H?Cicr_", "H?Ci[b_", "H?Ci[^o", and "H?KqKVO".

House of Graphs, Graph 536.
House of Graphs, Graph 36063.
Wikipedia, Graph toughness.

Cf. A003317, A366755.

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

A054595 Number of labeled 2-connected minimally 2-edge-connected graphs by nodes.

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A324418 Number of minimally 4-connected non-isomorphic n-vertex graphs.

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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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A366756 Number of minimally 1-tough unlabeled graphs on n nodes.

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

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