A simple unlabeled graph on vertices is called pancyclic if it contains cycles of all
lengths, 3, 4, ..., .
Since a pancyclic graph must contain a cycle of length , pancyclic graphs are of necessity Hamiltonian.

The numbers of pancyclic graphs on , 2, ... vertices are 0, 0, 1, 2, 7, 43, 372, 6132, 176797,
9302828, ... (OEIS A286684), the first few
of which are illustrated above.

George, J. C.; Khodkar, A.; and Wallis, W. D. Pancyclic
and Bipancyclic Graphs. Cham, Switzerland: Springer, 2016.Sloane,
N. J. A. Sequence A286684 in "The
On-Line Encyclopedia of Integer Sequences."