Definition: A graph G is bipartite if its vertices can be partitioned into two sets V1 and V2 and every edge joins a vertex in V1 with a vertex in V2. Bipartite graphs can be characterized by all circuits in such graphs having even length (if there are no circuits, the graph is also bipartite), where the length of a circuit or path is the number of edges in it What is the smallest bipartite graph?:
Depends on your definition, but if you define bipartite as two-colorable or having no odd cycles, then the empty graph or the trivial graph are the minimal bipartite graphs.
If by "smallest" you mean "number of vertices", then that is one possible answer.
But you could also remove the edge to leave two vertices and no edges, and perhaps you will consider this to be "smaller" than your example.