The fork graph, sometimes also called the chair graph, is the 5-vertex tree illustrated above. It could perhaps also be known as the 'h graph' (but not to be confused with the H graph).
The fork graph is nonhamiltonian since it is a connected bipartite graph whose bipartition classes have unequal sizes 2 and 3. It is also an untraceable graph since a traceable tree must be a path graph.
It is implemented in the Wolfram Language as GraphData["ForkGraph"].
)."