A008326 -id:A008326 - cp's OEIS frontend

A006823 Number of connected trivalent bipartite graphs with 2n nodes.

1, 1, 2, 5, 13, 38, 149, 703, 4132, 29579, 245627, 2291589, 23466857, 259974248, 3087698618, 39075020582, 524492748500, 7439833931266, 111179110620163, 1745593888011626, 28726140345832290, 494406533261250407, 8881990236308687928, 166255686198172837111, 3237191621055524796848, 65467841616499410561220

Offset: 3

N. J. A. Sloane and Brendan McKay

CRC Handbook of Combinatorial Designs, 1996, p. 648.
I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

G. Brinkmann, Fast generation of cubic graphs, Journal of Graph Theory, 23(2):139-149, 1996.
Nicolas Gastineau and Olivier Togni, S-Packing Colorings of Cubic Graphs, arXiv:1403:7495 [cs.DM], 2016.
Jan Goedgebeur and Patric R. J. Ostergard, Switching 3-Edge-Colorings of Cubic Graphs, arXiv:2105:01363 [math.CO], May 2021. See Table 2.
H. Gropp, On tactical configurations, regular bipartite graphs and (v,k,even)-designs, Discr. Math., 155 (1996), 81-98.
House of Graphs, Cubic bipartite graphs
M. Meringer, Tables of Regular Graphs
Eric Weisstein's World of Mathematics, Bicubic Graph [From _Eric W. Weisstein_, Jul 28 2009]

Column 3 of A008326.

Cf. A006824, A008325 (Euler transform).

Terms a(17) and beyond from Andrew Howroyd, Apr 03 2020

A008327 Triangle read by rows: T(n,k) is the number of simple regular bipartite graphs with 2n nodes and degree k, (0 <= k <= n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 4, 6, 4, 1, 1, 1, 1, 4, 14, 14, 4, 1, 1, 1, 1, 7, 41, 130, 41, 7, 1, 1, 1, 1, 8, 157, 1981, 1981, 157, 8, 1, 1, 1, 1, 12, 725, 62616, 304496, 62616, 725, 12, 1, 1, 1, 1, 14, 4196, 2806508, 78322916

Offset: 0

Brendan McKay

This sequence can be derived from A008326 by Euler transform. - Andrew Howroyd, Apr 03 2020

			Triangle begins:
  1,
  1, 1,
  1, 1, 1,
  1, 1, 1,   1,
  1, 1, 2,   1,    1,
  1, 1, 2,   2,    1,    1,
  1, 1, 4,   6,    4,    1,   1;
  1, 1, 4,  14,   14,    4,   1, 1;
  1, 1, 7,  41,  130,   41,   7, 1, 1;
  1, 1, 8, 157, 1981, 1981, 157, 8, 1, 1;
  ...

Andrew Howroyd, Table of n, a(n) for n = 0..189
B. D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.

Column k=0..5 are A000012, A000012, A002865, A008325, A333730, A333731.
Row sums are A008324.
Cf. A051031, A008326, A087114, A133687, A333159.

Column k is the Euler transform of column k of A008326. - Andrew Howroyd, Apr 03 2020

More terms from Eric Rogoyski, May 15 1997

Name clarified by Andrew Howroyd, Sep 05 2018

A006824 Number of connected regular bipartite graphs of degree 4 with 2n nodes.

Original entry on oeis.org

1, 1, 4, 14, 129, 1980, 62611, 2806490, 158937213, 10773251972, 855658082615, 78558949838723, 8251166737356319, 982806379842257309, 131756174189661102281, 19748565896506014747623, 3289970433888731383271400, 605948436052375098046655323, 122796503871896458570959144266

Offset: 4

N. J. A. Sloane

CRC Handbook of Combinatorial Designs, 1996, p. 648.
I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978.
H. Gropp, On tactical configurations, regular bipartite graphs and (v,k,even)-designs, Discr. Math., 155 (1996), 81-98.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

B. D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.
M. Meringer, Tables of Regular Graphs

Column 4 of A008326.

Cf. A006823, A006825, A333730.

Inverse Euler transform of A333730. - Andrew Howroyd, Apr 03 2020

Terms a(12) and beyond from Andrew Howroyd, Apr 03 2020

A006825 Number of connected regular bipartite graphs of degree 5 with 2n nodes.

Original entry on oeis.org

1, 1, 4, 41, 1981, 304495, 78322915, 27033154060, 11934777413004, 6593485023087880, 4485517185017428244, 3707462300996566329965, 3680029088808677189795063, 4341813441626419937873317841, 6033239205199247162872884404386, 9792722283774374706204648839780148

Offset: 5

N. J. A. Sloane

CRC Handbook of Combinatorial Designs, 1996, p. 648.
I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

M. Meringer, Tables of Regular Graphs
B. D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.

Column 5 of A008326.

Cf. A006823, A006824, A333731.

Inverse Euler transform of A333731. - Andrew Howroyd, Apr 03 2020

More terms from Eric Rogoyski, May 15 1997

Terms a(12) and beyond from Andrew Howroyd, Apr 03 2020

A008323 Number of simple connected regular bipartite graphs with 2n nodes.

Original entry on oeis.org

1, 1, 1, 2, 3, 5, 12, 34, 218, 4278, 431165, 162267174, 201636689352, 777816803938932, 9865957936943859185, 395886667549681686369527, 53716176608076643470380213991, 23524515269630339982914608683548933, 35682168849414944013547274439525153167248

Offset: 0

Brendan McKay

Brendan McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.

For n > 1, these are the row sums of triangle A008326.

Cf. A005142, A008324.

a(10) corrected and a(11) added by Brendan McKay, Sep 06 2018

a(0)=1 prepended and terms a(12) and beyond from Andrew Howroyd, Apr 03 2020

A014385 Number of connected regular bipartite graphs of degree 6 with 2n nodes.

Original entry on oeis.org

1, 1, 7, 157, 62616, 78322916, 147252447227, 376962851057234, 1280344203366849969, 5666901233595672365908, 32193489258177947645878365, 231605871969834571512497704231, 2084558172807256752718977250960988

Offset: 6

N. J. A. Sloane

CRC Handbook of Combinatorial Designs, 1996, p. 648.
I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978.

B. D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.

Column k=6 of A008326.

More terms from Eric Rogoyski, May 15 1997

a(12)-a(18) from Andrew Howroyd, Apr 04 2020

A014387 Number of connected regular bipartite graphs of degree 7 with 2n nodes.

Original entry on oeis.org

1, 1, 8, 725, 2806508, 27033154065, 376962851057235, 7292080848843162283, 192271946945501178473766, 6811960423672201527406129366, 320020341797819074616734725607588, 19688392653216509161510863093984500501

Offset: 7

N. J. A. Sloane

I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978.
CRC Handbook of Combinatorial Designs, 1996, p. 648.

B. D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.

Column k=7 of A008326.

More terms from Eric Rogoyski, May 15 1997

a(12)-a(18) from Andrew Howroyd, Apr 04 2020

cp's OEIS Frontend

A006823 Number of connected trivalent bipartite graphs with 2n nodes.

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A008327 Triangle read by rows: T(n,k) is the number of simple regular bipartite graphs with 2n nodes and degree k, (0 <= k <= n).

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A006824 Number of connected regular bipartite graphs of degree 4 with 2n nodes.

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A006825 Number of connected regular bipartite graphs of degree 5 with 2n nodes.

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A008323 Number of simple connected regular bipartite graphs with 2n nodes.

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A014385 Number of connected regular bipartite graphs of degree 6 with 2n nodes.

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A014387 Number of connected regular bipartite graphs of degree 7 with 2n nodes.

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