A pancyclic graph is a simple graph on 
vertices that contains
cycles of all lengths, 3, 4, ..., 
. Since a pancyclic graph must contain a graph
cycle of length 
,
pancyclic graphs are of necessity Hamiltonian.
The numbers of unlabeled 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.
Classes of graphs which are pancyclic include:
1. antiprism graphs,
2. Chang graphs,
4. Johnson graphs 
for 
and 
(Heidari and Mirafzal 2019),
5. Mathon graphs,
6. Paulus graphs,
8. complete sun graphs on 
vertices for 
,
9. tetrahedral graphs, and
10. wheel graphs on at least three vertices.
Pancyclic graphs that have exactly one graph cycle of each length are very rare and are known as uniquely pancyclic graphs.
A combination of graph toughness and a sufficiently large edge count forces pancyclicity. If 
is an integer and 
is a 
-tough connected
graph of graph order 
and edge count 
, then
 |
implies that 
is pancyclic (Jia et al. 2026).
-Tough Graphs." Elec. J. Combin. 33,
P3.78, 2026.