A001072 -id:A001072 - 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.

A324417 Number of minimally 10-edge-connected non-isomorphic n-vertex graphs.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 25, 2498

Offset: 1

Jens M. Schmidt, Mar 03 2019

Jens M. Schmidt, Data files in graph6 format

Cf. A001072, A324410.

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.

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.

A324410 Number of minimally 3-edge-connected non-isomorphic n-vertex graphs.

Original entry on oeis.org

0, 0, 0, 1, 1, 4, 8, 34, 118, 613, 3240, 20207

Offset: 1

Jens M. Schmidt, Feb 27 2019

Jens M. Schmidt, Data files in graph6 format

Cf. A001072, A324417.

A290011 Number of ways to connect n nodes with n+1 edges to form a 2-edge-connected graph.

Original entry on oeis.org

6, 85, 900, 9450, 104160, 1224720, 15422400, 207900000, 2993760000, 45924278400, 748280332800, 12913284384000, 235381386240000, 4520194398720000, 91233825306624000, 1931115968990208000, 42778526977105920000, 989887004576870400000, 23885015465274163200000

Offset: 4

Eugene Y. Q. Shen, Jul 17 2017

Robert Israel, Table of n, a(n) for n = 4..448

Cf. A001072, A052447, A054596, A095983

seq((n^2 + 2 *n - 18)* n!/24, n=6..30); # Robert Israel, Jul 19 2017

Table[(n - 4) (n!/8) + (n (n - 1)/2 - 3) (n!/12), {n, 4, 22}] (* Michael De Vlieger, Jul 18 2017 *)

a(n) = (n - 4)*(n!/8) + (n*(n - 1)/2 - 3)*(n!/12); \\ Michel Marcus, Jul 18 2017

a(n) = (n - 4)*(n!/8) + (n*(n - 1)/2 - 3)*(n!/12) = (n^2 + 2 n - 18)*(n!/24).

E.g.f.: x^4*(3*x^2+x-6)/(24*(x-1)^3). - Robert Israel, Jul 19 2017

A177451 Partial sums of A054595.

Original entry on oeis.org

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).

A324411 Number of minimally 4-edge-connected non-isomorphic n-vertex graphs.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 5, 17, 114, 940, 11275, 167504

Offset: 1

Jens M. Schmidt, Feb 27 2019

Jens M. Schmidt, Data files in graph6 format

Cf. A001072, A324417.

A324412 Number of minimally 5-edge-connected non-isomorphic n-vertex graphs.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 7, 32, 483, 10877, 386198

Offset: 1

Jens M. Schmidt, Feb 27 2019

Jens M. Schmidt, Data files in graph6 format

Cf. A001072, A324417.

A324413 Number of minimally 6-edge-connected non-isomorphic n-vertex graphs.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 1, 9, 71, 2516, 176323

Offset: 1

Jens M. Schmidt, Feb 27 2019

Jens M. Schmidt, Data files in graph6 format

Cf. A001072, A324417.

cp's OEIS Frontend

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

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A324417 Number of minimally 10-edge-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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A054596 Number of labeled minimally 2-edge-connected graphs by nodes.

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A324410 Number of minimally 3-edge-connected non-isomorphic n-vertex graphs.

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A290011 Number of ways to connect n nodes with n+1 edges to form a 2-edge-connected graph.

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A177451 Partial sums of A054595.

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A324411 Number of minimally 4-edge-connected non-isomorphic n-vertex graphs.

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A324412 Number of minimally 5-edge-connected non-isomorphic n-vertex graphs.

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A324413 Number of minimally 6-edge-connected non-isomorphic n-vertex graphs.

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