The Cameron cubic Hamiltonian graphs are a family of cubic planar Hamiltonian
graphs having exactly 3 Hamiltonian cycles
that were constructed by Kathleen Cameron (Cameron 2001; Knuth 2025, Problem 77).
The order-
Cameron cubic Hamiltonian graph has 
vertices. The first few are illustrated above.
Since they are cubic and contain exactly 3 Hamiltonian cycles, they are automatically perfectly
Hamiltonian. The 
and 
cases are Halin graphs. For
,
the graphs have exactly two graph automorphisms
(Knuth 2025).
For even 
,
each of the three Hamiltonian cycles gives a
bilaterally symmetric LCF embedding. "Nice"
LCF embeddings are shown above for 
to 5.
These graphs will be implemented in a future version of the Wolfram Language as GraphData[
"Cameron",
n]
.
They should not be confused with Cameron Graph, the 231-vertex strongly regular graph.
