The singleton graph is the graph consisting of a single isolated vertex with no edges.
It is therefore the empty graph on one vertex.
It is commonly denoted 
(i.e., the complete graph on one vertex).
The singleton graph is implemented in the Wolfram Language as GraphData["SingletonGraph"].
By convention, the singleton graph is considered to be Hamiltonian (B. McKay, pers. comm., Mar. 22, 2007).
