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0, 2, 0, 8, 137, 34464, 20

Gus Wiseman, <a href="/A326215/a326215.png">Non-isomorphic representatives of the a(4) = 20 Hamiltonian graphs with loops</a>.

Non-isomorphic representatives of the a(3) = 8 4 edge-sets:

{12,13,23}

{12,13,23,33}

{12,13,22,23,33}

{12,13,23} {11,12,13,23} {11,12,13,22,23} {11,12,13,22,23,33}

{11,12,31,32} {11,12,13,22,32}

{11,21,23,31} {11,12,22,31,32}

Non-isomorphic representatives of the a(3) = 8 edge-sets:

{12,13,23} {11,12,13,23} {11,12,13,22,23} {11,12,13,22,23,33}

{11,12,31,32} {11,12,13,22,32}

{11,21,23,31} {11,12,22,31,32}

allocated for Gus WisemanNumber of Hamiltonian unlabeled n-vertex graphs with loops.

0, 2, 0, 8, 137, 3446

0,2

A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once.

Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a>

The labeled case is A326240.

The directed case is A326226 (with loops) or A326225 (without loops).

The case without loops A003216.

Cf. A000088, A006125, A057864, A283420, A326239.

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Gus Wiseman, Jun 17 2019

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allocated for Gus Wiseman

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