I would like to know more about uniquely hamiltonian graphs with minimum vertex degree at least 3, and in particular what is the smallest one.

(Recall that a graph is *hamiltonian* if it has a cycle passing through each vertex exactly once each, and is *uniquely hamiltonian* if there is only one such cycle.)

Here's the smallest one that I currently know.

Does anyone know if a smaller one (fewer vertices) has been published?