A243393 -id:A243393 - 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

A243391 Number of isomorphism classes of connected 3-regular loopless multigraphs with n vertices and with semi-edges allowed.

Original entry on oeis.org

1, 3, 4, 12, 22, 68, 166, 534, 1589, 5464, 18579, 68320, 255424, 1000852, 4018156, 16671976, 70890940, 309439942, 1381815168, 6310880471, 29428287639, 140012980007, 678970863717, 3353545264060, 16857749613964, 86191265140699, 447951112379963, 2365177154077186

Offset: 1

Nico Van Cleemput, Jun 04 2014

nonn

a(n) is also the number of isomorphism classes of connected loopless multigraphs with n vertices of degree 3 or less. - Andrew Howroyd, Mar 20 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.

Column k=3 of A334546.

Cf. A000421, A243392, A243393, A243394, A303030.

a(23)-a(28) from Andrew Howroyd, Mar 20 2020

A303032 Number of unlabeled connected graphs with n nodes of degree 5 or less.

Original entry on oeis.org

1, 1, 1, 2, 6, 21, 112, 697, 6386, 75700, 1156842, 21503340, 471142472, 11851753163, 336605142326, 10661879669294, 373171677147769, 14326039970010402, 599529134063451455, 27206654007549974712, 1332697569146848014994, 70181910345392508318643, 3959059626001669328959513

Offset: 0

Natan Arie Consigli, Jun 04 2018

nonn

Cf. A303031 (also counts double edged graphs), A303033 (at most triple edges).

Cf. A121941 (degree 4 or less), A243393 (degree 3 or less).

for n in {1..12}; do geng -c -D5 ${n} -u; done

a(13)-a(22) from Andrew Howroyd, Mar 20 2020

A243394 Number of isomorphism classes of connected 3-regular multigraphs with n vertices and with loops and semi-edges allowed.

Original entry on oeis.org

2, 5, 7, 22, 43, 141, 373, 1270, 4053, 14671, 52826, 203289, 795581, 3241367, 13504130, 57904671, 253856990, 1139231977, 5219113084, 24401837085, 116278408069, 564380686932, 2787884851040, 14007277302822, 71538337097031, 371197207327709, 1955833646495247, 10459788214042492

Offset: 1

Nico Van Cleemput, Jun 04 2014

nonn

a(n) is also the number of isomorphism classes of connected multigraphs with n vertices of degree 3 or less and with loops allowed. - Andrew Howroyd, Mar 21 2020

G. Brinkmann, N. Van Cleemput, T. Pisanski, Generation of various classes of trivalent graphs, Theoretical Computer Science 502, 2013, pp.16-29.

Cf. A000421, A005967, A243391, A243392, A243393, A243394.

a(23)-a(28) from Andrew Howroyd, Mar 21 2020

cp's OEIS Frontend

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

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A243391 Number of isomorphism classes of connected 3-regular loopless multigraphs with n vertices and with semi-edges allowed.

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A303032 Number of unlabeled connected graphs with n nodes of degree 5 or less.

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A243394 Number of isomorphism classes of connected 3-regular multigraphs with n vertices and with loops and semi-edges allowed.

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