A303032 -id:A303032 - cp's OEIS frontend

A121941 Number of unlabeled connected simple graphs with n nodes of degree 4 or less.

1, 1, 1, 2, 6, 21, 78, 353, 1929, 12207, 89402, 739335, 6800637, 68531618, 748592936, 8788983173, 110201690911, 1468157196474, 20695559603921, 307590282700915, 4805537369573319, 78710267083015571, 1348394635886684901, 24109112440149231355, 449050443283294835914

Offset: 0

Parthasarathy Nambi, Sep 03 2006

Number of graphs of hydrogen bonded water clusters.
This counts the connected graphs where each vertex has degree 4 or less. - Charles R Greathouse IV, Jul 07 2017
Also number of saturated hydrocarbons and allotropes with n carbon, or valence 4, atoms (excluding stereoisomers) following the octet rule. - Natan Arie Consigli, Jul 07 2017

			With 4 carbons, n-butane, i-butane, cyclobutane, bicyclobutane, methylcyclopropane and tetrahedrane are the 6 isomers satisfying the property above, so a(4)=6. - _Natan Arie Consigli_, Jul 07 2017
If n=5 then the number of graphs of hydrogen bonded water clusters is 21.

G. Brinkmann, Generating water clusters and other directed graphs, J. Math. Chem. 46 (4) (2009) 1112-1121, Table 1.
T. Miyake and M. Aida, Enumeration of topology-distinct structures of hydrogen bonded water clusters, Chem. Phys. Lett., vol. 363 (2002) pp. 106-110. See Table 1 column 2 on page 109.

Cf. A121942, A243393 (degree 3 or less), A287424 (excludes allotropes), A289157, A289158, A303032 (degree 5 or less).

nauty
```
geng -c -D4 ${n} -q | multig -m1 -D4 -u
```

More terms sent by Natan Arie Consigli, Jul 07 2017
Renamed by Andrew Howroyd, Mar 19 2020 based on comment by Charles R Greathouse IV.
a(16)-a(24) from Andrew Howroyd, Mar 19 2020

A303031 Number of unlabeled connected loopless multigraphs with n nodes of degree 5 or less and with single or double edges.

Original entry on oeis.org

1, 1, 2, 7, 43, 282, 2708, 31175, 451701, 7731154, 154264825, 3515514725, 90381251065, 2594105950453, 82437061616923, 2880328250160638, 109987239823116870, 4566153786442575091, 205144850920195457266, 9933105076082553631262, 516439104253062357469829

Offset: 0

Natan Arie Consigli, Jun 04 2018

nonn

Cf. A289158, A303032, A303033.

for n in {1..11}; do geng -c -D5 ${n}  -q | multig -m2 -D5 -u; done

a(12)-a(20) from Andrew Howroyd, Mar 20 2020

A243393 Number of isomorphism classes of connected 3-regular loopless simple graphs with n vertices and with semi-edges allowed.

Original entry on oeis.org

1, 1, 2, 6, 10, 29, 64, 194, 531, 1733, 5524, 19430, 69322, 262044, 1016740, 4101318, 16996157, 72556640, 317558689, 1424644848, 6536588420, 30647561117, 146647344812, 715511358833, 3556531372395, 17996244725780, 92634418530686, 484756161038264

Offset: 1

Nico Van Cleemput, Jun 04 2014

nonn

Also: number of isomorphism classes of connected loopless simple graphs with maximum degree at most 3. - Brendan McKay, Mar 11 2020

Nino Bašić and Ivan Damnjanović, On cubic polycirculant nut graphs, arXiv:2411.16904 [math.CO], 2024. See p. 22.
Gunnar Brinkmann, Nico Van Cleemput, and Tomaž Pisanski, Generation of various classes of trivalent graphs, Theoretical Comp. Sci. (2013) Vol. 502, 16-29.

Cf. A121941, A243391, A243392, A243394, A303032.

a(24)-a(28) from Andrew Howroyd, Mar 20 2020

A303033 Number of unlabeled connected loopless multigraphs with n nodes of degree 5 or less and with single, double or triple edges.

Original entry on oeis.org

1, 1, 3, 12, 81, 535, 5274, 60684, 869238, 14595645, 284939257, 6347472749, 159579271688, 4482770916274, 139578090353236, 4783834092385411, 179397242557917048, 7322223973235272082, 323760818899998259561, 15443359560966718348986, 791699492870169123493379

Offset: 0

Natan Arie Consigli, Jun 04 2018

nonn

Cf. A134818, A303030, A303031, A303032.

for n in {1..11}; do geng -c -D5 ${n}  -q | multig  -m3 -D5 -u;

a(12)-a(20) from Andrew Howroyd, Mar 20 2020

A334547 Number of unlabeled connected loopless multigraphs with n nodes of degree 5 or less.

Original entry on oeis.org

1, 1, 5, 14, 93, 602, 5847, 66289, 937696, 15575285, 301360805, 6663874305, 166516898890, 4654082023569, 144301649717895, 4928171085359360, 184252862642720722, 7501009857590958129, 330928677041195111955, 15754816518916261088582, 806306082299053607173143

Offset: 0

Andrew Howroyd, May 05 2020

nonn

Column k=5 of A334546.

Cf. A303031, A303032, A303033, A333896.

Inverse Euler transform of A333896.

cp's OEIS Frontend

A121941 Number of unlabeled connected simple graphs with n nodes of degree 4 or less.

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A303031 Number of unlabeled connected loopless multigraphs with n nodes of degree 5 or less and with single or double edges.

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A243393 Number of isomorphism classes of connected 3-regular loopless simple graphs with n vertices and with semi-edges allowed.

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A303033 Number of unlabeled connected loopless multigraphs with n nodes of degree 5 or less and with single, double or triple edges.

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nauty

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A334547 Number of unlabeled connected loopless multigraphs with n nodes of degree 5 or less.

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