Pancyclic Graph
A simple unlabeled graph on 
vertices is called pancyclic if it contains cycles of all lengths, 3, 4, ..., 
. Since they must contain a cycle of length 
, pancyclic graphs are 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.
REFERENCES
Sloane, N. J. A. Sequence A286684 in "The On-Line Encyclopedia of Integer Sequences."
