A325447 -id:A325447 - cp's OEIS frontend

A003216 Number of Hamiltonian graphs with n nodes.

1, 0, 1, 3, 8, 48, 383, 6196, 177083, 9305118, 883156024, 152522187830, 48322518340547

Offset: 1

a(1) could also be taken to be 0, but I prefer a(1) = 1. - N. J. A. Sloane, Oct 15 2006

J. P. Dolch, Names of Hamiltonian graphs, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 259-271.
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 219.
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

John Asplund, N. Bradley Fox, and Arran Hamm, New Perspectives on Neighborhood-Prime Labelings of Graphs, arXiv:1804.02473 [math.CO], 2018.
J. P. Dolch, Names of Hamiltonian graphs, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 259-271. (Annotated scanned copy of 3 pages)
Scott Garrabrant and Igor Pak, Pattern Avoidance is Not P-Recursive, preprint, 2015.
Scott Garrabrant and Igor Pak, Pattern Avoidance is Not P-Recursive, arXiv:1505.06508 [math.CO], 2015.
Jan Goedgebeur, Barbara Meersman, and Carol T. Zamfirescu, Graphs with few Hamiltonian Cycles, arXiv:1812.05650 [math.CO], 2018-2019.
Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
Eric Weisstein's World of Mathematics, Hamiltonian Graph
Wikipedia, Hamiltonian path
Gus Wiseman, Non-isomorphic representatives of the a(5) = 8 simple graphs containing a Hamiltonian cycle.

Main diagonal of A325455 and of A325447 (for n>=3).
The labeled case is A326208.
The directed case is A326226 (with loops) or A326225 (without loops).
The case without loops is A326215.
Unlabeled simple graphs not containing a Hamiltonian cycle are A246446.
Unlabeled simple graphs containing a Hamiltonian path are A057864.
Cf. A000088, A006125, A283420.

A000088(n) = a(n) + A246446(n). - Gus Wiseman, Jun 17 2019

Extended to n=11 by Brendan McKay, Jul 15 1996
a(12) from Sean A. Irvine, Mar 17 2015
a(13) from A246446 added by Jan Goedgebeur, Sep 07 2019

A325455 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with circumference k, (n >= 3, k >= 3).

Original entry on oeis.org

1, 1, 3, 4, 6, 8, 10, 24, 24, 48, 30, 87, 116, 226, 383, 83, 342, 527, 1283, 2663, 6196, 257, 1324, 2644, 6644, 17613, 55468, 177083

Offset: 3

Andrew Howroyd, Sep 06 2019

Trees are excluded since they do not have any cycle.

			Triangle begins:
    1;
    1,    3;
    4,    6,    8;
   10,   24,   24,   48;
   30,   87,  116,  226,   383;
   83,  342,  527, 1283,  2663,  6196;
  257, 1324, 2644, 6644, 17613, 55468, 177083;
  ...

Eric Weisstein's World of Mathematics, Graph Circumference
Eric Weisstein's World of Mathematics, Hamiltonian Graph

Right diagonal is A003216.
Row sums are A241841.
Cf. A128042, A309524, A325447.

cp's OEIS Frontend

A003216 Number of Hamiltonian graphs with n nodes.

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